Over breakfast at your hotel you read an article berating banks about the fraudulent credit card transactions they let through. You proceed to check out and bang! Your credit card is rejected because (as you find out later) the bank thought [1] it couldn’t possibly be you in that exotic place. Ah, those banks! They accept too much. Ah, those banks! They reject too much. Finding the right balance is a case of soundness versus precision.
Similar notions are essential to the design of tools for program analysis, looking for such suspicious cases as dead code (program parts that will never be executed). An analysis can be sound, or not; it can be complete, or not.
These widely used concepts are sometimes misunderstood. The first answer I get when innocently asking people whether the concepts are clear is yes, of course, everyone knows! Then, as I bring up such examples as credit card rejection or dead code detection, assurance quickly yields to confusion. One sign that things are not going well is when people start throwing in terms like “true positive” and “false negative”. By then any prospect of reaching a clear conclusion has vanished. I hope that after reading this article you will never again (in a program analysis context) be tempted to use them.
Now the basic idea is simple. An analysis is sound if it reports all errors, and complete if it only reports errors. If not complete, it is all the more precise that it reports fewer non-errors.
You can stop here and not be too far off [2]. But a more nuanced and precise discussion helps.
1. A relative notion
As an example of common confusion, one often encounters attempts to help through something like Figure 1, which cannot be right since it implies that all sound methods are complete. (We’ll have better pictures below.)
![](data:image/png;base64,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)
Figure 1: Naïve (and wrong) illustration
Perhaps this example can be dismissed as just a bad use of illustrations [3] but consider the example of looking for dead code. If the analysis wrongly determines that some reachable code is unreachable, is it unsound or incomplete?
With this statement of the question, the only answer is: it depends!
It depends on the analyzer’s mandate:
- If it is a code checker that alerts programmers to cases of bad programming style, it is incomplete: it reports as an error a case that is not. (Reporting that unreachable code is reachable would cause unsoundness, by missing a case that it should have reported.)
- If it is the dead-code-removal algorithm of an optimizing compiler, which will remove unreachable code, it is unsound: the compiler will remove code that it should not. (Reporting that unreachable code is reachable would cause incompleteness, by depriving the compiler of an optimization.)
As another example, consider an analyzer that finds out whether a program will terminate. (If you are thinking “but that can’t be done!“, see the section “Appendix: about termination” at the very end of this article.) If it says a program does not terminates when in fact it does, is it unsound or incomplete?
Again, that depends on what the analyzer seeks to establish. If it is about the correctness of a plain input-to-output program (a program that produces results and then is done), we get incompleteness: the analyzer wrongly flags a program that is actually OK. But if it is about verifying that continuously running programs, such as the control system for a factory, will not stop (“liveness”), then the analyzer is unsound.
Examples are not limited to program analysis. A fraud-indentification process that occasionally rejects a legitimate credit card purchase is, from the viewpoint of preserving the bank from fraudulent purchases, incomplete. From the viewpoint of the customer who understands a credit card as an instrument enabling payments as long as you have sufficient credit, it is unsound.
These examples suffice to show that there cannot be absolute definitions of soundness and precision: the determination depends on which version of a boolean property we consider desirable. This decision is human and subjective. Dead code is desirable for the optimizing compiler and undesirable (we will say it is a violation) for the style checker. Termination is desirable for input-output programs and a violation for continuously running programs.
Once we have decided which cases are desirable and which are violations, we can define the concepts without any ambiguity: soundness means rejecting all violations, and completeness means accepting all desirables.
While this definition is in line with the unpretentious, informal one in the introduction, it makes two critical aspects explicit:
- Relativity. Everything depends on an explicit decision of what is desirable and what is a violation. Do you want customers always to be able to use their credit cards for legitimate purchases, or do you want to detect all frauds attempts?
- Duality. If you reverse the definitions of desirable and violation (they are the negation of each other), you automatically reverse the concepts of soundness and completeness and the associated properties.
We will now explore the consequences of these observations.
2. Theory and practice
For all sufficiently interesting problems, theoretical limits (known as Rice’s theorem) ensure that it is impossible to obtain both soundness and completeness.
But it is not good enough to say “we must be ready to renounce either soundness or completeness”. After all, it is very easy to obtain soundness if we forsake completeness: reject every case. A termination-enforcement analyzer can reject every program as potentially non-terminating. A bank that is concerned with fraud can reject every transaction (this seems to be my bank’s approach when I am traveling) as potentially fraudulent. Dually, it is easy to ensure completeness if we just sacrifice soundness: accept every case.
These extreme theoretical solutions are useless in practice; here we need to temper the theory with considerations of an engineering nature.
The practical situation is not as symmetric as the concept of duality theoretically suggests. If we have to sacrifice one of the two goals, it is generally better to accept some incompleteness: getting false alarms (spurious reports about cases that turn out to be harmless) is less damaging than missing errors. Soundness, in other words, is essential.
Even on the soundness side, though, practice tempers principle. We have to take into account the engineering reality of how tools get produced. Take a program analyzer. In principle it should cover the entire programming language. In practice, it will be built step by step: initially, it may not handle advanced features such as exceptions, or dynamic mechanisms such as reflection (a particularly hard nut to crack). So we may have to trade soundness for what has been called “soundiness” [4], meaning soundness outside of cases that the technology cannot handle yet.
If practical considerations lead us to more tolerance on the soundness side, on the completeness side they drag us (duality strikes again) in the opposite direction. Authors of analysis tools have much less flexibility than the theory would suggest. Actually, close to none. In principle, as noted, false alarms do not cause catastrophes, as missed violations do; but in practice they can be almost as bad. Anyone who has ever worked on or with a static analyzer, going back to the venerable Lint analyzer for C, knows the golden rule: false alarms kill an analyzer. When people discover the tool and run it for the first time, they are thrilled to discover how it spots some harmful pattern in their program. What counts is what happens in subsequent runs. If the useful gems among the analyzer’s diagnostics are lost in a flood of irrelevant warnings, forget about the tool. People just do not have the patience to sift through the results. In practice any analysis tool has to be darn close to completeness if it has to stand any chance of adoption.
Completeness, the absence of false alarms, is an all-or-nothing property. Since in the general case we cannot achieve it if we also want soundness, the engineering approach suggests using a numerical rather than boolean criterion: precision. We may define the precision pr as 1 – im where im is the imprecision: the proportion of false alarms.
The theory of classification defines precision differently: as pr = tp / (tp + fp), where tp is the number of false positives and fp the number of true positives. (Then im would be fp / (tp + fp).) We will come back to this definition, which requires some tuning for program analyzers.
From classification theory also comes the notion of recall: tp / (tp + fn) where fn is the number of false negatives. In the kind of application that we are looking at, recall corresponds to soundness, taken not as a boolean property (“is my program sound?“) but a quantitative one (“how sound is my program?“). The degree of unsoundness un would then be fn / (tp + fn).
3. Rigorous definitions
With the benefit of the preceding definitions, we can illustrate the concepts, correctly this time. Figure 2 shows two different divisions of the set of U of call cases (universe):
- Some cases are desirable (D) and others are violations (V).
- We would like to know which are which, but we have no way of finding out the exact answer, so instead we run an analysis which passes some cases (P) and rejects some others (R).
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)
Figure 2: All cases, classified
The first classification, left versus right columns in Figure 2, is how things are (the reality). The second classification, top versus bottom rows, is how we try to assess them. Then we get four possible categories:
- In two categories, marked in green, assessment hits reality on the nail: accepted desirables (A), rightly passed, and caught violations (C), rightly rejected.
- In the other two, marked in red, the assessment is off the mark: missed violations (M), wrongly passed; and false alarms (F), wrongly accepted.
The following properties hold, where U (Universe) is the set of all cases and ⊕ is disjoint union [5]:
— Properties applicable to all cases:
U = D ⊕ V
U = P ⊕ R
D = A ⊕ F
V = C ⊕ M
P = A ⊕ M
R = C ⊕ F
U = A ⊕M ⊕ F ⊕ C
We also see how to define the precision pr: as the proportion of actual violations to reported violations, that is, the size of C relative to R. With the convention that u is the size of U and so on, then pr = c / r, that is to say:
- pr = c / (c + f) — Precision
- im = f / (c + f) — Imprecision
We can similarly define soundness in its quantitative variant (recall):
- so = a / (a + m) — Soundness (quantitative)
- un = m / (a + m) — Unsoundness
These properties reflect the full duality of soundness and completeness. If we reverse our (subjective) criterion of what makes a case desirable or a violation, everything else gets swapped too, as follows:
![](data:image/png;base64,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)
Figure 3: Duality
We will say that properties paired this way “dual” each other [6].
It is just as important (perhaps as a symptom that things are not as obvious as sometimes assumed) to note which properties do not dual. The most important examples are the concepts of “true” and “false” as used in “true positive” etc. These expressions are all the more confusing that the concepts of True and False do dual each other in the standard duality of Boolean algebra (where True duals False, Or duals And, and an expression duals its negation). In “true positive” or “false negative”, “true” and “false” do not mean True and False: they mean cases in which (see figure 2 again) the assessment respectively matches or does not match the reality. Under duality we reverse the criteria in both the reality and the assessment; but matching remains matching! The green areas remain green and the red areas remain red.
The dual of positive is negative, but the dual of true is true and the dual of false is false (in the sense in which those terms are used here: matching or not). So the dual of true positive is true negative, not false negative, and so on. Hereby lies the source of the endless confusions.
The terminology of this article removes these confusions. Desirable duals violation, passed duals rejected, the green areas dual each other and the red areas dual each other.
4. Sound and complete analyses
If we define an ideal world as one in which assessment matches reality [7], then figure 2 would simplify to just two possibilities, the green areas:
![](data:image/png;base64,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)
Figure 4: Perfect analysis (sound and complete)
This scheme has the following properties:
— Properties of a perfect (sound and complete) analysis as in Figure 4:
M = ∅ — No missed violations
F = ∅ — No false alarms
P = D — Identify desirables exactly
R = V –Identify violations exactly
As we have seen, however, the perfect analysis is usually impossible. We can choose to build a sound solution, potentially incomplete:
![](data:image/png;base64,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)
Figure 5: Sound desirability analysis, not complete
In this case:
— Properties of a sound analysis (not necessarily complete) as in Figure 5:
M = ∅ — No missed violations
P = A — Accept only desirables
V = C — Catch all violations
P ⊆ D — Under-approximate desirables
R ⊇ V — Over-approximate violations
Note the last two properties. In the perfect solution, the properties P = D and R = V mean that the assessment, yielding P and V, exactly matches the reality, D and V. From now on we settle for assessments that approximate the sets of interest: under-approximations, where the assessment is guaranteed to compute no more than the reality, and over-approximations, where it computes no less. In all cases the assessed sets are either subsets or supersets of their counterparts. (Non-strict, i.e. ⊆ and ⊇ rather than ⊂ and ⊃; “approximation” means possible approximation. We may on occasion be lucky and capture reality exactly.)
We can go dual and reach for completeness at the price of possible unsoundness:
![](data:image/png;base64,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)
Figure 6: Complete desirability analysis, not sound
The properties are dualled too:
— Properties of a complete analysis (not necessarily sound), as in Figure 6:
F = ∅ — No false alarms
R = C — Reject only violations
D = A — Accept all desirables
P ⊇ D — Over-approximate desirables
R ⊆ V — Under-approximate violations
5. Desirability analysis versus violation analysis
We saw above why the terms “true positives”, “false negatives” etc., which do not cause any qualms in classification theory, are deceptive when applied to the kind of pass/fail analysis (desirables versus violations) of interest here. The definition of precision provides further evidence of the damage. Figure 7 takes us back to the general case of Figure 2 (for analysis that is guaranteed neither sound nor complete) but adds these terms to the respective categories.
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)
Figure 7: Desirability analysis (same as fig. 2 with added labeling)
The analyzer checks for a certain desirable property, so if it wrongly reports a violation (F) that is a false negative, and if it misses a violation (M) it is a false positive. In the definition from classification theory (section 2, with abbreviations standing for True/False Positives/Negatives): TP = A, FP = M, FN = F, TN = C, and similarly for the set sizes: tp = a, fp = m, fn = f, tn = c.
The definition of precision from classification theory was pr = tp / (tp + fp), which here gives a / (a + m). This cannot be right! Precision has to do with how close the analysis is to completeness, that is to day, catching all violations.
Is classification theory wrong? Of course not. It is simply that, just as Alice stepped on the wrong side of the mirror, we stepped on the wrong side of duality. Figures 2 and 7 describe desirability analysis: checking that a tool does something good. We assess non-fraud from the bank’s viewpoint, not the stranded customer’s; termination of input-to-output programs, not continuously running ones; code reachability for a static checker, not an optimizing compiler. Then, as seen in section 3, a / (a + m) describes not precision but soundness (in its quantitative interpretation, the parameter called “so” above).
To restore the link with classification theory , we simply have to go dual and take the viewpoint of violation analysis. If we are looking for possible violations, the picture looks like this:
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)
Figure 8: Violation analysis (same as fig. 7 with different positive/negative labeling)
Then everything falls into place: tp = c, fp = f, fn = m, tn = a, and the classical definition of precision as pr = tp / (tp + fp) yields c / (c + f) as we are entitled to expect.
In truth there should have been no confusion since we always have the same picture, going back to Figure 2, which accurately covers all cases and supports both interpretations: desirability analysis and violation analysis. The confusion, as noted, comes from using the duality-resistant “true”/”false” opposition.
To avoid such needless confusion, we should use the four categories of the present discussion: accepted desirables, false alarms, caught violations and missed violations [8]. Figure 2 and its variants clearly show the duality, given explicitly in Figure 3, and sustains interpretations both for desirability analysis and for violation analysis. Soundness and completeness are simply special cases of the general framework, obtained by ruling out one of the cases of incorrect analysis in each of Figures 4 and 5. The set-theoretical properties listed after Figure 2 express the key concepts and remain applicable in all variants. Precision c / (c + f) and quantitative soundness a / (a + m) have unambiguous definitions matching intuition.
The discussion is, I hope, sound. I have tried to make it complete. Well, at least it is precise.
Notes and references
[1] Actually it’s not your bank that “thinks” so but its wonderful new “Artificial Intelligence” program. ⤣
[2] For a discussion of these concepts as used in testing see Mauro Pezzè and Michal Young, Software Testing and Analysis: Process, Principles and Techniques, Wiley, 2008. ⤣
[3] Edward E. Tufte: The Visual Display of Quantitative Information, 2nd edition, Graphics Press, 2001.⤣
[4] Michael Hicks,What is soundness (in static analysis)?, blog article available here, October 2017. ⤣
[5] The disjoint union property X = Y ⊕ Z means that Y ∩ Z = ∅ (Y and Z are disjoint) and X = Y ∪ Z (together, they yield X). ⤣
[6] I thought this article would mark the introduction into the English language of “dual” as a verb, but no, it already exists in the sense of turning a road from one-lane to two-lane (dual). ⤣
[7] As immortalized in a toast from the cult movie The Prisoner of the Caucasus: “My great-grandfather says: I have the desire to buy a house, but I do not have the possibility. I have the possibility to buy a goat, but I do not have the desire. So let us drink to the matching of our desires with our possibilities.” See 6:52 in the version with English subtitles. ⤣
[8] To be fully consistent we should replace the term “false alarm” by rejected desirable. I is have retained it because it is so well established and, with the rest of the terminology as presented, does not cause confusion. ⤣
[9] Byron Cook, Andreas Podelski, Andrey Rybalchenko: Proving Program Termination, in Communications of the ACM, May 2011, Vol. 54 No. 5, Pages 88-98. ⤣
Background and acknowledgments
This reflection arose from ongoing work on static analysis of OO structures, when I needed to write formal proofs of soundness and completeness and found that the definitions of these concepts are more subtle than commonly assumed. I almost renounced writing the present article when I saw Michael Hicks’s contribution [4]; it is illuminating, but I felt there was still something to add. For example, Hicks’s set-based illustration is correct but still in my opinion too complex; I believe that the simple 2 x 2 pictures used above convey the ideas more clearly. On substance, his presentation and others that I have seen do not explicitly mention duality, which in my view is the key concept at work here.
I am grateful to Carlo Ghezzi for enlightening discussions, and benefited from comments by Alexandr Naumchev and others from the Software Engineering Laboratory at Innopolis University.
Appendix: about termination
With apologies to readers who have known all of the following from kindergarten: a statement such as (section 1): “consider an analyzer that finds out whether a program will terminate” can elicit no particular reaction (the enviable bliss of ignorance) or the shocked rejoinder that such an analyzer is impossible because termination (the “halting” problem) is undecidable. This reaction is just as incorrect as the first. The undecidability result for the halting problem says that it is impossible to write a general termination analyzer that will always provide the right answer, in the sense of both soundness and completeness, for any program in a realistic programming language. But that does not preclude writing termination analyzers that answer the question correctly, in finite time, for given programs. After all it is not hard to write an analyzer that will tell us that the program from do_nothing until True loop do_nothing end will terminate and that the program from do_nothing until False loop do_nothing end will not terminate. In the practice of software verification today, analyzers can give such sound answers for very large classes of programs, particularly with some help from programmers who can obligingly provide variants (loop variants, recursion variants). For a look into the state of the art on termination, see the beautiful survey by Cook, Podelski and Rybalchenko [9].
Also appears in the Communications of the ACM blog
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