How do you know a program does what you intended?

Part of this is being clear about what you intended (by writing  specifications , for example), but your intents, however clear, are not enough: you need evidence that your intents were correctly expressed computationally. To get this evidence, we do  verification .

There are many ways to verify code. A reasonable first instinct is to simply run your program. After all, what better way to check whether you expressed your intents then to see with your own eyes what your program does? This is an empirical approach is called  testing . Some testing is  manual , in that a human executes a program and verifies that it does what was intended. Some testing is  automated , in that the test is run automatically by a computer. Another way to verify code is to  analyze  it, using logic to verify its correct operation. As with testing, some analysis is  manual , since humans do it. We call this manual analysis  inspection , whereas other analysis is  automated , since computers do it. We call this  program analysis . This leads to a nice complementary set of verification technique along two axes: degree of automation and type of verification:

• Manual techniques include  manual testing  (which is empirical) and  inspections  (which is analytical)
• Automated techniques include  automated testing  (which is empirical) and  program analysis  (which is analytical)

To discuss each of these and their tradeoffs, first we have to cover some theory about verification. The first and simplest ideas are some terminology:

• A  defect  is some subset of a program’s code that exhibits behavior that violates a program’s specifications. For example, if a program was supposed to sort a list of numbers in increasing order and print it to a console, but a flipped inequality in the sorting algorithm made it sort them in decreasing order, the flipped inequality is the defect.
• A  failure  is the program behavior that results from a defect executing. In our sorting example, the failure is the incorrectly sorted list printed on the console.
• A  bug  vaguely refers to either the defect, the failure, or both. When we say “bug”, we’re not being very precise, but it is a popular shorthand for a defect and everything it causes.

Note that because defects are defined relative to  intent , whether a behavior is a failure depends entirely the definition of intent. If that intent is vague, whether something is a defect is vague. Moreover, you can define intents that result in behaviors that seem like failures: for example, I can write a program that intentionally crashes. A crash isn’t a failure if it was intended! This might be pedantic, but you’d be surprised how many times I’ve seen professional developers in bug triage meetings say:

“Well, it’s worked this way for a long time, and people have built up a lot of workarounds for this bug. It’s also really hard to fix. Let’s just call this by design. Closing this bug as won’t fix.”

Testing

So how do you  find  defects in a program? Let’s start with testing. Testing is generally the easiest kind of verification to do, but as a practice, it has questionable efficacy. Empirical studies of testing find that it  is  related to fewer defects in the future, but not strongly related, and it’s entirely possible that it’s not the testing itself that results in fewer defects, but that other activities (such as more careful implementation) result in fewer defects and testing efforts ^{1 1}

Iftekhar Ahmed, Rahul Gopinath, Caius Brindescu, Alex Groce, and Carlos Jensen (2016). Can testedness be effectively measured?. ACM SIGSOFT Foundations of Software Engineering (FSE).

Why is this? One possibility is that  no amount of testing can prove a program correct with respect to its specifications . Why? It boils down to the same limitations that exist in science: with empiricism, we can provide evidence that a program  does  have defects, but we can’t provide complete evidence that a program  doesn’t  have defects. This is because even simple programs can execute in a infinite number of different ways.

Consider this JavaScript program:

The function should always return 0, right? How many possible values of  input  do we have to try manually to verify that it always does? Well, if  input  is an integer, then there are 2 to the power 32 possible integer values, because JavaScript uses 32-bits to represent an integer. That’s not infinite, but that’s a lot. But what if  input  is a string? There are an infinite number of possible strings because they can have any sequence of characters of any length. Now we have to manually test an infinite number of possible inputs. So if we were restricting ourselves to testing, we will never know that the program is correct for all possible inputs. In this case, automatic testing doesn’t even help, since there are an infinite number of tests to run.

There are some ideas in testing that can improve how well we can find defects. For example, rather than just testing the inputs you can think of, focus on all of the lines of code in your program. If you find a set of tests that can cause all of the lines of code to execute, you have one notion of  test coverage . Of course, lines of code aren’t enough, because an individual line can contain multiple different paths in it (e.g.,  value ? getResult1() : getResult2() ). So another notion of coverage is executing all of the possible  control flow paths  through the various conditionals in your program. Executing  all  of the possible paths is hard, of course, because every conditional in your program doubles the number of possible paths (you have 200 if statements in your program? That’s up to 2 to the power 200 possible paths, which is more paths than there are  atoms in the universe .

There are many types of testing that are common in software engineering:

• Unit tests  verify that functions return the correct output. For example, a program that implemented a function for finding the day of the week for a given date might also include unit tests that verify for a large number of dates that the correct day of the week is returned. They’re good for ensuring widely used low-level functionality is correct.
• Integration tests  verify that when all of the functionality of a program is put together into the final product, it behaves according to specifications. Integration tests often operate at the level of user interfaces, clicking buttons, entering text, submitting forms, and verifying that the expected feedback always occurs. Integration tests are good for ensuring that important tasks that users will perform are correct.
• Regression tests  verify that behavior that previously worked doesn’t stop working. For example, imagine you find a defect that causes logins to fail; you might write a test that verifies that this cause of login failure does not occur, in case someone breaks the same functionality again, even for a different reason. Regression tests are good for ensuring that you don’t break things when you make changes to your application.

Which tests you should write depends on what risks you want to take. Don’t care about failures? Don’t write any tests. If failures of a particular kind are highly consequential to your team, you should probably write tests that check for those failures. As we noted above, you can’t write enough tests to catch all bugs, so deciding which tests to write and maintain is a key challenge.

Analysis

Now, you might be thinking that it’s obvious that the program above is defective for some integers and strings. How did you know? You  analyzed  the program rather than executing it with specific inputs. For example, when I read (analyzed) the program, I thought:

“if we assume  input  is an integer, then there are only three types of values to meaningfully consider with respect to the  >  in the loop condition: positive, zero, and negative. Positive numbers will always decrement to 0 and return 0. Zero will return zero. And negative numbers just get returned as is, since they’re less then zero, which is wrong with respect to the specification. And in JavaScript, strings are never greater than 0 (let’s not worry about whether it even makes sense to be able to compare strings and numbers), so the string is returned, which is wrong.”

The above is basically an informal proof. I used logic to divide the possible states of  input  and their effect on the program’s behavior. I used  symbolic execution  to verify all possible paths through the function, finding the paths that result in correct and incorrect values. The strategy was an inspection because we did it manually. If we had written a  program  that read the program to perform this proof automatically, we would have called it  program analysis .

The benefits of analysis is that it  can  demonstrate that a program is correct in all cases. This is because they can handle infinite spaces of possible inputs by mapping those infinite inputs onto a finite space of possible executions. It’s not always possible to do this in practice, since many kinds of programs  can  execute in infinite ways, but it gets us closer to proving correctness.

One popular type of automatic program analysis tools is a  static analysis  tool. These tools read programs and identify potential defects using the types of formal proofs like the ones above. They typically result in a set of warnings, each one requiring inspection by a developer to verify, since some of the warnings may be false positives (something the tool thought was a defect, but wasn’t). Although static analysis tools can find many kinds of defects, they aren’t yet viewed by developers to be that useful because the false positives are often large in number and the way they are presented make them difficult to understand ^{4 4}

Brittany Johnson, Yoonki Song, Emerson Murphy-Hill, and Robert Bowdidge (2013). Why don't software developers use static analysis tools to find bugs?. ACM/IEEE International Conference on Software Engineering.

Not all analytical techniques rely entirely on logic. In fact, one of the most popular methods of verification in industry are  code reviews , also known as  inspections . The basic idea of an inspection is to read the program analytically, following the control and data flow inside the code to look for defects. This can be done alone, in groups, and even included as part of process of integrating changes, to verify them before they are committed to a branch. Modern code reviews, while informal, help find defects, stimulate knowledge transfer between developers, increase team awareness, and help identify alternative implementations that can improve quality ^{2 2}

Alberto Bacchelli and Christian Bird (2013). Expectations, outcomes, and challenges of modern code review. ACM/IEEE International Conference on Software Engineering.

Beyond these more technical considerations around verifying a program’s correctness are organizational issues around different software qualities. For example, different organizations have different sensitivities to defects. If a $0.99 game on the app store has a defect, that might not hurt its sales much, unless that defect prevents a player from completing the game. If Boeing’s flight automation software has a defect, hundreds of people might die. The game developer might do a little manual play testing, release, and see if anyone reports a defect. Boeing will spend years proving mathematically with automatic program analysis that every line of code does what is intended, and repeating this verification every time a line of code changes. Moreover, requirements may change differently in different domains. For example, a game company might finally recognize the sexist stereotypes amplified in its game mechanics and have to change requirements, resulting in changed definitions of correctness, and the incorporation of new software qualities such as bias into testing plans. Similarly, Boeing might have to respond to pandemic fears by having to shift resources away from verifying flight crash safety to verifying public health safety. What type of verification is right for your team depends entirely on what a team is building, who’s using it, and how they’re depending on it.