Bertrand Meyer's technology+ blog

My group, the Chair of Software Engineering, at the newly created Schaffhausen Institute of Technology has open positions for both PhD students and postdocs. We are looking for candidates with a passion for reliable software and a mix of theoretical knowledge and practical experience in software engineering. Candidates should have degrees in computer science or related fields: a doctorate for postdoc positions, a master’s degree for PhD positions. Postdoc candidates should have a substantial publication record. Experience in one or more of the following fields is a plus:

• Software verification (axiomatic, model-checking, abstract interpretation etc.).
• Advanced techniques of software testing.
• Formal methods, semantics of programming languages, type theory.
• Design by Contract, Eiffel, techniques of correctness-by-construction.
• Cybersecurity.

 Compensation at both levels is attractive. The PhD program is conducted in cooperation with partner universities. 

 Interested candidates should send a CV and relevant documents or links to bm@sit.org. They are also welcome to contact me for details.

About this article: it originated as a series of posts on the Communications of the ACM blog. I normally repost such articles here. (Even though copy-paste is usually not good, there are three reasons for this duplication: the readership seems to be largely disjoint; I can use better formatting, since their blog software is more restrictive than WordPress; and it is good to have a single repository for all my articles, including both those who originated on CACM and those who did not.) The series took the form of nine articles, where each of the first few ended with a quiz, to which the next one, published a couple of days later, provided an answer. Since all these answers are now available it would make no sense to use the same scheme, so I am instead publishing the whole thing as a single article  with nine sections, slightly adapted from the original.

I was too lazy so far to collect all the references into a single list, so numbers such as [1] refer to the list at the end of the corresponding section.

A colleague recently asked me to present a short overview of  axiomatic semantics as a guest lecture in one of his courses. I have been teaching courses on software verification for a long time (see e.g. here), so I have plenty of material; but instead of just reusing it, I decided to spend a bit of time on explaining why it is good to have a systematic approach to software verification. Here is the resulting tutorial.

1. Introduction and attempt #1

Say “software verification” to software professionals, or computer science students outside of a few elite departments, and most of them will think  “testing”. In a job interview, for example, show a loop-based algorithm to a programmer and ask “how would you verify it?”: most will start talking about devising clever test cases.

Far from me to berate testing [1]; in fact, I have always thought that the inevitable Dijkstra quote about testing — that it can only show the presence of errors, not their absence [2] — which everyone seems to take as an indictment and dismissal of testing (and which its author probably intended that way) is actually a fantastic advertisement for testing: a way to find bugs? Yes! Great! Where do I get it?  But that is not the same as verifying the software, which means attempting to ascertain that it has no bugs.

Until listeners realize that verification cannot just mean testing, the best course material on axiomatic semantics or other proof techniques will not attract any interest. In fact, there is somewhere a video of a talk by the great testing and public-speaking guru James Whittaker where he starts by telling his audience not to worry, this won’t be a standard boring lecture, he will not start talking about loop invariants [3]! (Loop invariants are coming in this article, in fact they are one of its central concepts, but in later sections only, so don’t bring the sleeping bags yet.) I decided to start my lecture by giving an example of what happens when you do not use proper verification. More than one example, in fact, as you will see.

A warning about this article: there is nothing new here. I am using an example from my 1990 book Introduction to the Theory of Programming Languages (exercise 9.12). Going even further back, a 1983 “Programming Pearls” Communications of the ACM article by Jon Bentley [4] addresses the same example with the same basic ideas. Yet almost forty years later these ideas are still not widely known among practitioners. So consider these articles as yet another tutorial on fundamental software engineering stuff.

The tutorial is a quiz. We start with a program text:

from

i := 1 ; j := n              — Result initialized to 0.

until i = j loop

m := (i + j) // 2         — Integer division

if t [m] ≤ x then i := m  else  j := m end

end

if x = t [i] then Result := i end

All variables are of integer type. t is an up-sorted array of integers, indexed from 1 to n . We do not let any notation get between friends. A loop from p until e loop q end executes p then, repeatedly: stops if e (the exit condition) is true, otherwise executes q. (Like {p ; while not e do {q}} in some other notations.) “:=” is assignment, “=” equality testing.  “//” is integer division, e.g. 6 //3 = 7 //3 = 2. Result is the name of a special variable whose final value will be returned by this computation (as part of a function, but we only look at the body). Result is automatically initialized to zero like all integer variables, so if execution does not assign anything to Result the function will return zero.

First question: what is this program trying to do?

OK, this is not the real quiz. I assume you know the answer: it is an attempt at “binary search”, which finds an element in the array, or determines its absence, in a sequence of about log₂ (n) steps, rather than n if we were use sequential search.  (Remember we assume the array is sorted.) Result should give us a position where x appears in the array, if it does, and otherwise be zero.

Now for the real quiz: does this program meet this goal?

The answer should be either yes or no. (If no, I am not asking for a correct version, at least not yet, and in any case you can find some in the literature.) The situation is very non-symmetric, we might say Popperian:

• To justify a no answer it suffices of a single example, a particular array t and a particular value x, for which the program fails to set Result as it should.
• To justify a yes answer we need to provide a credible argument that for every t and  x the program sets Result as it should.

Notes to section 1

[1] The TAP conference series (Tests And Proofs), which Yuri Gurevich and I started, explores the complementarity between the two approaches.

[2] Dijkstra first published his observation in 1969. He did not need consider the case of infinite input sets: even for a trivial finite program that multiplies two 32-bit integers, the number of cases to be examined, 2⁶⁴, is beyond human reach. More so today with 64-bit integers. Looking at this from a 2020 perspective, we may note that exhaustive testing of a finite set of cases, which Dijkstra dismissed as impossible in practice, is in fact exactly what the respected model checking verification technique does; not on the original program, but on a simplified — abstracted — version precisely designed to keep the number of cases tractable. Dijkstra’s argument remains valid, of course, for  the original program if non-trivial. And model-checking does not get us out of the woods: while we are safe if its “testing” finds no bug, if it does find one we have to ensure that the bug is a property of the original program rather than an artifact of the abstraction process.

[3] It is somewhere on YouTube, although I cannot find it right now.

[4] Jon Bentley: Programming Pearls: Writing Correct Programs, in Communications of the ACM, vol. 26, no. 12, pp. 1040-1045, December 1983, available for example here.

2. Attempt #2

Was program #1 correct? If so it should yield the correct answer. (An answer is correct if either Result is the index in t of an element equal to x, or Result = 0 and x does not appear in t.)

This program is not correct. To prove that it is not correct it suffices of a single example (test case) for which the program does not  “yield the correct answer”. Assume x = 1 and the array t has two elements both equal to zero (n = 2, remember that arrays are indexed from 1):

t = [0   0]

The successive values of the variables and expressions are:

                                            m       i          j            i + j + 1

After initialization:                   1         2                3

i ≠ j, so enter loop:           1       1        2                 6         — First branch of “if” since t [1] ≤ x
— so i gets assigned the value of m

But then neither of the values of i and j has changed, so the loop will repeat its body identically (taking the first branch) forever. It is not even that the program yields an incorrect answer: it does not yield an answer at all!

Note (in reference to the famous Dijkstra quote mentioned in the first article), that while it is common to pit tests against proofs, a test can actually be a proof: a test that fails is a proof that the program is incorrect. As valid as the most complex mathematical proof. It may not be the kind of proof we like most (our customers tend to prefer a guarantee that the program is correct), but it is a proof all right.

We are now ready for the second attempt:

—  Program attempt #2.

from

i := 1 ; j := n

until i = j or Result > 0  loop

m := (i + j) // 2         — Integer division

if t [m] ≤ x then

i := m  + 1

elseif t [m] = x then

Result := m

else                         — In this case t [m] > x

j := m – 1

end

end

Unlike the previous one this version always changes i or j, so we may hope it does not loop forever. It has a nice symmetry between i and j.

Same question as before: does this program meet its goal?

3. Attempt #3

The question about program #2, as about program #1: was: it right?

Again no.  A trivial example disproves it: n = 1, the array t contains a single element t [1] = 0, x = 0. Then the initialization sets both i and j to 1, i = j holds on entry to the loop which stops immediately, but Result is zero whereas it should be 1 (the place where x appears).

Here now is attempt #3, let us see it if fares better:

—  Program attempt #3.

from

i := 1 ; j := n

until i = j loop

m := (i + j + 1) // 2

if t [m] ≤ x then

i := m  + 1

else

j := m

end

end

if 1  ≤ i  and i ≤ n then Result := i end
       — If not, Result remains 0.

What about this one?

3. Attempt #4 (also includes 3′)

The first two program attempts were wrong. What about the third?

I know, you have every right to be upset at me, but the answer is no once more.

Consider a two-element array t = [0 0] (so n = 2, remember that our arrays are indexed from 1 by convention) and a search value x = 1. The successive values of the variables and expressions are:

                                                  m          i          j            i + j + 1

After initialization:                            1        2           4

i ≠ j, so enter loop:               2           3        2          6                  — First branch of “if” since t [2] < x

i ≠ j,  enter loop again:        3           ⚠                                       — Out-of-bounds memory access!
— (trying to access non-existent t [3])

Oops!

Note that we could hope to get rid of the array overflow by initializing i to 0 rather than 1. This variant (version #3′) is left as a bonus question to the patient reader. (Hint: it is also not correct. Find a counter-example.)

OK, this has to end at some point. What about the following version (#4): is it right?

—  Program attempt #4.

from

i := 0 ; j := n + 1

until i = j loop

m := (i + j) // 2

if t [m] ≤ x then

i := m  + 1

else

j := m

end

end

if 1 ≤ i  and i ≤ n then Result := i end

5. Attempt #5

Yes, I know, this is dragging on. But that’s part of the idea: witnessing how hard it is to get a program right if you just judging by the seat of your pants. Maybe we can get it right this time?

Are we there yet? Is program attempt #4 finally correct?

Sorry to disappoint, but no. Consider a two-element array t = [0 0], so n = 2, and a search value x = 1 (yes, same counter-example as last time, although here we could also use x = 0). The successive values of the variables and expressions are:

                                                 m          i          j            i + j

After initialization:                           0        3           3

i ≠ j, so enter loop:               1           2       3          5            — First branch of “if”

i ≠ j, enter loop again:         2         3        3         6            — First branch again

i = j, exit loop

The condition of the final “if” is true, so Result gets the value 3. This is quite wrong, since there is no element at position 3, and in any case x does not appear in t.

But we are so close! Something like this should work, should it not?

So patience, patience, let us tweak it just one trifle more, OK?

—  Program attempt #5.

from

i := 0 ; j := n

until i ≥ j or Result > 0 loop

m := (i + j) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

Does it work now?

6. Attempt #6

The question about program #5  was the same as before: is it right, is it wrong?

Well, I know you are growing more upset at me with each section, but the answer is still that this program is wrong. But the way it is wrong is somewhat specific; and it applies, in fact, to all previous variants as well.

This particular wrongness (fancy word for “bug”) has a history. As I pointed out in the first article, there is a long tradition of using binary search to illustrate software correctness issues. A number of versions were published and proved correct, including one in the justly admired Programming Pearls series by Jon Bentley. Then in 2006 Joshua Bloch, then at Google, published a now legendary blog article [2] which showed that all these versions suffered from a major flaw: to obtain m, the approximate mid-point between i and j, they compute

(i + j) // 2

which, working on computer integers rather than mathematical integers, might overflow! This in a situation in which both i and j, and hence m as well, are well within the range of the computer’s representable integers, 2^-n to 2ⁿ (give or take 1) where n is typically 31 or, these days, 63, so that there is no conceptual justification for the overflow.

In the specification that I have used for this article, i starts at 1, so the problem will only arise for an array that occupies half of the memory or more, which is a rather extreme case (but still should be handled properly). In the general case, it is often useful to use arrays with arbitrary bounds (as in Eiffel), so we can have even a small array, with high indices, for which the computation will produce an overflow and bad results.

The Bloch gotcha is a stark reminder that in considering the correctness of programs we must include all relevant aspects and consider programs as they are executed on a real computer, not as we wish they were executed in an ideal model world.

(Note that Jon Bentley alluded to this requirement in his original article: while he did not explicitly mention integer overflow, he felt it necessary to complement his proof by the comment that that  “As laborious as our proof of binary search was, it is still unfinished by some standards. How would you prove that the program is free of runtime errors (such as division by zero, word overflow, or array indices out of bounds)?” Prescient words!)

It is easy to correct the potential arithmetic overflow bug: instead of (i + j) // 2, Bloch suggested we compute the average as

i + (j – i) // 2

which is the same from a mathematician’s viewpoint, and indeed will compute the same value if both variants compute one, but will not overflow if both i and j are within range.

So we are ready for version 6, which is the same as version 5 save for that single change:

—  Program attempt #6.

from

i := 0 ; j := n

until i ≥ j or Result > 0 loop

m := i + (j – i) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

Now is probably the right time to recall the words by which Donald Knuth introduces binary search in the original 1973 tome on Sorting and Searching of his seminal book series The Art of Computer Programming:

Although the basic idea of binary search is comparatively straightforward, the details can be somewhat tricky, and many good programmers have done it wrong the first few times they tried.

Do you need more convincing? Be careful what you answer, I have more variants up my sleeve and can come up with many more almost-right-but-actually-wrong program attempts if you nudge me. But OK, even the best things have an end. This is not the last section yet, but that was the last program attempt. To the naturally following next question in this running quiz,  “is version 6 right or wrong”, I can provide the answer: it is, to the best of my knowledge, a correct program. Yes! [3].

But the quiz continues. Since answers to the previous questions were all  that the programs were not correct, it sufficed in each case to find one case for which the program did not behave as expected. Our next question is of a different nature: can you find an argument why version #6 is correct?

References for section 6

[1] (In particular) Jon Bentley: Programming Pearls — Writing Correct Programs, in Communications of the ACM, vol. 26, no. 12, December 1983, pages 1040-1045, available here.

[2] Joshua Bloch: Extra, Extra — Read All About It: Nearly All Binary Searches and Mergesorts are Broken, blog post, on the Google AI Blog, 2 June 2006, available here.

[3] A caveat: the program is correct barring any typos or copy-paste errors — I am starting from rigorously verified programs (see the next posts), but the blogging system’s UI and text processing facilities are not the best possible for entering precise technical text such as code. However carefully I check, I cannot rule out a clerical mistake, which of course would be corrected as soon as it is identified.

7. Using a program prover

Preceding sections presented candidate binary search algorithms and asked whether they are correct. “Correct” means something quite precise: that for an array t and a value x, the final value of the variable Result is a valid index of t (that is to say, is between 1 and n, the size of t) if and only if x appears at that index in t.

The last section boldly stated that program attempt #6 was correct. The question was: why?

In the case of the preceding versions, which were incorrect, you could prove that property, and I do mean prove, simply by exhibiting a single counter-example: a single t and x for which the program does not correctly set Result. Now that I asserting the program to be correct, one example, or a million examples, do not suffice. In fact they are almost irrelevant. Test as much as you like and get correct results every time, you cannot get rid of the gnawing fear that if you had just tested one more time after the millionth test you would have produced a failure. Since the set of possible tests is infinite there is no solution in sight [1].

We need a proof.

I am going to explain that proof in the next section, but before that I would like to give you an opportunity to look at the proof by yourself. I wrote in one of the earlier articles that most of what I have to say was already present in Jon Bentley’s 1983 Programming Pearls contribution [2], but a dramatic change did occur in the four decades since: the appearance of automated proof system that can handle significant, realistic programs. One such system, AutoProof, was developed at the Chair of Software engineering at ETH Zurich [3] (key project members were Carlo Furia, Martin Nordio, Nadia Polikarpova and Julian Tschannen, with initial contributions by Bernd Schoeller) on the basis of the Boogie proof technology from Microsoft Research).

AutoProof is available for online use, and it turns out that one of the basic tutorial examples is binary search. You can go to the corresponding page and run the proof.

I am going to let you try this out (and, if you are curious, other online AutoProof examples as well) without too many explanations; those will come in the next section. Let me simply name the basic proof technique: loop invariant. A loop invariant is a property INV associated with a loop, such that:

• A. After the loop’s initialization, INV will hold.
• B. One execution of the loop’s body, if started with INV satisfied (and the loop’s exit condition not satisfied, otherwise we wouldn’t be executing the body!), satisfies INV again when it terminates.

This idea is of course the same as that of a proof by induction in mathematics: the initialization corresponds to the base step (proving that P (0) holds) and the body property to the induction step (proving that from P (n) follows P (n + 1). With a traditional induction proof we deduce that the property (P (n)) holds for all integers. For the loop, we deduce that when the loop finishes its execution:

• The invariant still holds, since executing the loop means executing the initialization once then the loop body zero or more times.
• And of course the exit condition also holds, since otherwise we would still be looping.

That is how we prove the correctness of a loop: the conjunction of the invariant and the exit condition must yield the property that we seek (in the example, the property, stated above of Result relative to t and x).

We also need to prove that the loop does terminate. This part involves another concept, the loop’s variant, which I will explain in the next section.

For the moment I will not say anything more and let you look at the AutoProof example page (again, you will find it here), run the verification, and read the invariant and other formal elements in the code.

To “run the verification” just click the Verify button on the page. Let me emphasize (and emphasize again and again and again) that clicking Verify will not run the code. There is no execution engine in AutoProof, and the verification does not use any test cases. It processes the text of the program as it appears on the page and below. It applies mathematical techniques to perform the proof; the core property to be proved is that the proposed loop invariant is indeed invariant (i.e. satisfies properties A and B above).

The program being proved on the AutoProof example page is version #6 from the last section, with different variable names. So far for brevity I have used short names such as i, j and m but the program on the AutoProof site applies good naming practices with variables called low, up, middle and the like. So here is that version again with the new variable names:

—  Program attempt #7  (identical to #6 with different variable names) .

from

low := 0 ; up := n

until low ≥ up or Result > 0 loop

middle := low + ((up – low) // 2)

if a [middle] < value then      — The array is now called a rather than t

low := middle + 1

elseif  a [middle] > value then

up := middle

else

Result := middle

end

end

This is exactly the algorithm text on the AutoProof page, the one that you are invited to let AutoProof verify for you. I wrote “algorithm text” rather than “program text” because the actual program text (in Eiffel) includes variant and invariant clauses which do not affect the program’s execution but make the proof possible.

Whether or not these concepts (invariant, variant, program proof) are completely new to you, do try the prover and take a look at the proof-supporting clauses. In the next article I will remove any remaining mystery.

Note and references for section 7

[1] Technically the set of possible [array, value] pairs is finite, but of a size defying human abilities. As I pointed out in the first section, the “model checking” and “abstract interpretation” verification techniques actually attempt to perform an exhaustive test anyway, after drastically reducing the size of the search space. That will be for some other article.

[2]  Jon Bentley: Programming Pearls: Writing Correct Programs, in Communications of the ACM, vol. 26, no. 12, pp. 1040-1045, December 1983, available for example here.

[3] The AutoProof page contains documentations and numerous article references.

8. Understanding the proof

The previous section invited you to run the verification on the AutoProof tutorial page dedicated to the example. AutoProof is an automated proof system for programs. This is just a matter of clicking  “Verify”, but more importantly, you should read the annotations added to the program text, particularly the loop invariant, which make the verification possible. (To avoid any confusion let me emphasize once more that clicking “Verify” does not run the program, and that no test cases are used; the effect is to run the verifier, which attempts to prove the correctness of the program by working solely on the program text.)

Here is the program text again, reverting for brevity to the shorter identifiers (the version on the AutoProof page has more expressive ones):

from

i := 0 ; j := n

until i ≥ j or Result > 0 loop

m := i + (j – i) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

Let us now see what makes the proof possible. The key property is the loop invariant, which reads

A:   1  ≤ i  ≤ j  ≤ n + 1
B:   0  ≤ Result  ≤ n
C:   ∀ k: 1 .. i –1  |  t [k] < x
D:   ∀ k: j .. n  |  t [k] > x
E:    (Result > 0)   ⇒   (t [Result] = x)

The notation is slightly different on the Web page to adapt to the Eiffel language as it existed at the time it was produced; in today’s Eiffel you can write the invariant almost as shown above. Long live Unicode, allowing us to use symbols such as ∀ (obtained not by typing them but by using smart completion, e.g. you start typing “forall” and you can select the ∀ symbol that pops up), ⇒ for  “implies” and many others

Remember that the invariant has to be established by the loop’s initialization and preserved by every iteration. The role of each of its clauses is as follows:

• A: keep the indices in range.
• B: keep the variable Result, whose final value will be returned by the function, in range.
• C and D: eliminate index intervals in which we have determined that the sought value, x, does not appear. Before i, array values are smaller; starting at j, they are greater. So these two intervals, 1..i and j..n, cannot contain the sought value. The overall idea of the algorithm (and most other search algorithms) is to extend one of these two intervals, so as to narrow down the remaining part of 1..n where x may appear.
• E: express that as soon as we find a positive (non-zero) Result, its value is an index in the array (see B) where x does appear.

Why is this invariant useful? The answer is that on exit it gives us what we want from the algorithm. The exit condition, recalled above, is

i ≥ j or Result > 0

Combined with the invariant, it tells us that on exit one of the following will hold:

• Result > 0, but then because of E we know that x appears at position Result.
• i < j, but then A,  C and D  imply that x does not appear anywhere in t. In that case it cannot be true that Result > 0, but then because of B Result must be zero.

What AutoProof proves, mechanically, is that under the function’s precondition (that the array is sorted):

• The initialization ensures the invariant.
• The loop body, assuming that the invariant is satisfied but the exit condition is not, ensures the loop invariant again after it executes.
• The combination of the invariant and the exit condition ensures, as just explained, the postcondition of the function (the property that Result will either be positive and the index of an element equal to x, or zero with the guarantee that x appears nowhere in t).

Such a proof guarantees the correctness of the program if it terminates. We (and AutoProof) must prove separately that it does terminate. The technique is simple: find a “loop variant”, an integer quantity v  which remains non-negative throughout the loop (in other words, the loop invariant includes or implies v ≥ 0) and decreases on each iteration, so that the loop cannot continue executing forever. An obvious variant here is j – i + 1 (where the + 1 is needed because j – i may go down to -1 on the last iteration if x does not appear in the array). It reflects the informal idea of the algorithm: repeatedly decrease an interval i .. j – 1 (initially, 1 .. n) guaranteed to be such that x appears in t if and only if it appears at an index in that interval. At the end, either we already found x or the interval is empty, implying that x does not appear at all.

A great reference on variants and the techniques for proving program termination is a Communications of the ACM article of 2011: [3].

The variant gives an upper bound on the number of iterations that remain at any time. In sequential search, j – i + 1 would be our best bet; but for binary search it is easy to show that  log₂  (j – i + 1) is also a variant, extending the proof of correctness with a proof of performance (the key goal of binary search being to ensure a logarithmic rather than linear execution time).

This example is, I hope, enough to highlight the crucial role of loop invariants and loop variants in reasoning about loops. How did we get the invariant? It looks like I pulled it out of a hat. But in fact if we go the other way round (as advocated in classic books [1] [2]) and develop the invariant and the loop together the process unfolds itself naturally and there is nothing mysterious about the invariant.

Here I cannot resist quoting (thirty years on!) from my own book Introduction to the Theory of Programming Languages [4]. It has a chapter on axiomatic semantics (also known as Hoare logic, the basis for the ideas used in this discussion), which I just made available: see here [5]. Its exercise 9.12 is the starting point for this series of articles. Here is how the book explains how to design the program and the invariant [6]:

In the general case [of search, binary or not] we aim for a loop body of the form

m := ‘‘Some value in 1.. n such that i ≤ m < j’’;

if t [m] ≤ x then

i := m + 1

else

j := m

end

It is essential to get all the details right (and easy to get some wrong):

• The instruction must always decrease the variant j – i, by increasing i or decreasing j. If the the definition of m specified just m ≤ j rather than m < j, the second branch would not meet this goal.
•  This does not transpose directly to i: requiring i < m < j would lead to an impossibility when j – i is equal to 1. So we accept i ≤ m but then we must take m + 1, not m, as the new value of i in the first branch.
•  The conditional’s guards are tests on t [m], so m must always be in the interval 1 . . n. This follows from the clause 0 ≤ i ≤ j ≤ n + 1 which is part of the invariant.
•  If this clause is satisfied, then m ≤ n and m > 0, so the conditional instruction indeed leaves this clause invariant.
• You are invited to check that both branches of the conditional also preserve the rest of the invariant.
• Any policy for choosing m is acceptable if it conforms to the above scheme. Two simple choices are i  and j – 1; they lead to variants of the sequential search algorithm [which the book discussed just before binary search].

For binary search, m will be roughly equal to the average of i and j.

“Roughly” because we need an integer, hence the // (integer division).

In the last section, I will reflect further on the lessons we can draw from this example, and the practical significance of the key concept of invariant.

References and notes for section 8

[1] E.W. Dijkstra: A Discipline of Programming, Prentice Hall, 1976.

[2] David Gries: The Science of Programming, Springer, 1989.

[3] Byron Cook, Andreas  Podelski and Andrey Rybalchenko: Proving program termination, in Communications of the ACM, vol. 54, no. 11, May 2011, pages 88-98, available here.

[4] Bertrand Meyer, Introduction to the Theory of Programming Languages, Prentice Hall, 1990. The book is out of print but can be found used, e.g. on Amazon. See the next entry for an electronic version of two chapters.

[5] Bertrand Meyer Axiomatic semantics, chapter 9 from [3], available here. Note that the PDF was reconstructed from an old text-processing system (troff); the figures could not be recreated and are missing. (One of these days I might have the patience of scanning them from a book copy and adding them. Unless someone wants to help.) I also put online, with the same caveat, chapter 2 on notations and mathematical basis: see here.

[6] Page 383 of [4] and [5]. The text is verbatim except a slight adaptation of the programming notation and a replacement of the variables: i in the book corresponds to i – 1 here, and j to j – 1. As a matter of fact I prefer the original conventions from the book (purely as a matter of taste, since the two are rigorously equivalent), but I changed here to the conventions of the program as it appears in the AutoProof page, with the obvious advantage that you can verify it mechanically. The text extract is otherwise exactly as in the 1990 book.

9. Lessons learned

What was this journey about?

We started with a succession of attempts that might have “felt right” but were in fact all wrong, each in its own way: giving the wrong answer in some cases, crashing (by trying to access an array outside of its index interval) in some cases, looping forever in some cases. Always “in some cases”,  evidencing the limits of testing, which can never guarantee that it exercises all the problem cases. A correct program is one that works in all cases. The final version was correct; you were able to prove its correctness with an online tool and then to understand (I hope) what lies behind that proof.

To show how to prove such correctness properties, I have referred throughout the series to publications from the 1990s (my own Introduction to The Theory of Programming Languages), the 1980s (Jon Bentley’s Programming Pearls columns, Gries’s Science of Programming), and even the 1970s (Dijkstra’s Discipline of Programming). I noted that the essence of my argument appeared in a different form in one of Bentley’s Communications articles. What is the same and what has changed?

The core concepts have been known for a long time and remain applicable: assertion, invariant, variant and a few others, although they are much better understood today thanks to decades of theoretical work to solidify the foundation. Termination also has a more satisfactory theory.

On the practical side, however, the progress has been momentous. Considerable engineering has gone into making sure that the techniques scaled up. At the time of Bentley’s article, binary search was typical of the kind of programs that could be proved correct, and the proof had to proceed manually. Today, we can tackle much bigger programs, and use tools to perform the verification.

Choosing binary search again as an example today has the obvious advantage that everyone can understand all the details, but should not be construed as representative of the state of the art. Today’s proof systems are far more sophisticated. Entire operating systems, for example, have been mechanically (that is to say, through a software tool) proved correct. In the AutoProof case, a major achievement was the proof of correctness [1] of an entire data structure (collections) library, EiffelBase 2. In that case, the challenge was not so much size (about 8,000 source lines of code), but the complexity of both:

• The scope of the verification, involving the full range of mechanisms of a modern object-oriented programming language, with classes,  inheritance (single and multiple), polymorphism, dynamic binding, generics, exception handling etc.
• The code itself, using sophisticated data structures and algorithms, involving in particular advanced pointer manipulations.

In both cases, progress has required advances on both the science and engineering sides. For example, the early work on program verification assumed a bare-bones programming language, with assignments, conditionals, loops, routines, and not much more. But real programs use many other constructs, growing ever richer as programming languages develop. To cover exception handling in AutoProof required both theoretical modeling of this construct (which appeared in [2]) and implementation work.

More generally, scaling up verification capabilities from the small examples of 30 years ago to the sophisticated software that can be verified today required the considerable effort of an entire community. AutoProof, for example, sits at the top of a tool stack relying on the Boogie environment from Microsoft Research, itself relying on the Z3 theorem prover. Many person-decades of work make the result possible.

Beyond the tools, the concepts are esssential. One of them, loop invariants, has been illustrated in the final version of our program. I noted in the first article the example of a well-known expert and speaker on testing who found no better way to announce that a video would not be boring than  “relax, we are not going to talk about loop invariants.” Funny perhaps, but unfair. Loop invariants are one of the most beautiful concepts of computer science. Not so surprisingly, because loop invariants are the application to programming of the concept of mathematical induction. According to the great mathematician Henri Poincaré, all of mathematics rests on induction; maybe he exaggerated, maybe not, but who would think of teaching mathematics without explaining induction? Teaching programming without explaining loop invariants is no better.

Below is an illustration (if you will accept my psychedelic diagram) of what a loop is about, as a problem-solving technique. Sometimes we can get the solution directly. Sometimes we identify several steps to the solution; then we use a sequence (A ; B; C). Sometimes we can find two (or more) different ways of solving the problem in different cases; then we use a conditional (if c then A else B end). And sometimes we can only get a solution by getting closer repeatedly, not necessarily knowing in advance how many times we will have to advance towards it; then, we use a loop.

We identify an often large (i.e. very general) area where we know the solution will lie; we call that area the loop invariant. The solution or solutions (there may be more than one) will have to satisfy a certain condition; we call it the exit condition. From wherever we are, we shoot into the invariant region, using an appropriate operation; we call it the initialization. Then we execute as many times as needed (maybe zero if our first shot was lucky) an operation that gets us closer to that goal; we call it the loop body. To guarantee termination, we must have some kind of upper bound of the distance to the goal, decreasing each time discretely; we call it the loop variant.

This explanation is only an illustration, but I hope it makes the ideas intuitive. The key to a loop is its invariant. As the figure suggests, the invariant is always a generalization of the goal. For example, in binary search (and many other search algorithms, such as sequential search), our goal is to find a position where either x appears or, if it does not, we can be sure that it appears nowhere. The invariant says that we have an interval with the same properties (either x appears at a position belonging to that interval or, if it does not, it appears nowhere). It obviously includes the goal as a special case: if the interval has length 1, it defines a single position.

An invariant should be:

1. Strong enough that we can devise an exit condition which in the end, combined with the invariant, gives us the goal we seek (a solution).
2. Weak enough that we can devise an initialization that ensures it (by shooting into the yellow area) easily.
3. Tuned so that we can devise a loop body that, from a state satifying the invariant, gets us to a new one that is closer to the goal.

In the example:

1. The exit condition is simply that the interval’s length is 1. (Technically, that we have computed Result as the single interval element.) Then from the invariant and the exit condition, we get the goal we want.
2. Initialization is easy, since we can just take the initial interval to be the whole index range of the array, which trivially satisfies the invariant.
3. The loop body simply decreases the length of the interval (which can serve as loop variant to ensure termination). How we decrease the length depends on the search strategy; in sequential search, each iteration decreases the length by 1, correct although not fast, and binary search decreases it by about half.

The general scheme always applies. Every loop algorithm is characterized by an invariant. The invariant may be called the DNA of the algorithm.

To demonstrate the relevance of this principle, my colleagues Furia, Velder, and I published a survey paper [6] in ACM Computing Surveys describing the invariants of important algorithms in many areas of computer science, from search algorithms to sorting (all major algorithms), arithmetic (long integer addition, squaring), optimization and dynamic programming  (Knapsack, Levenshtein/Edit distance), computational geometry (rotating calipers), Web (Page Rank)… I find it pleasurable and rewarding to go deeper into the basis of loop algorithms and understand their invariants; like a geologist who does not stop at admiring the mountain, but gets to understand how it came to be.

Such techniques are inevitable if we want to get our programs right, the topic of this article. Even putting aside the Bloch average-computation overflow issue, I started with 5 program attempts, all kind of friendly-looking but wrong in different ways. I could have continued fiddling with the details, following my gut feeling to fix the flaws and running more and more tests. Such an approach can be reasonable in some cases (if you have an algorithm covering a well-known and small set of cases), but will not work for non-trivial algorithms.

Newcomers to the concept of loop invariant sometimes panic: “this is all fine, you gave me the invariants in your examples, how do I find my own invariants for my own loops?” I do not have a magic  recipe (nor does anyone else), but there is no reason to be scared. Once you have understood the concept and examined enough examples (just a few of those in [6] should be enough), writing the invariant at the same time as you are devising a loop will come as a second nature to you.

As the fumbling attempts in the first few sections should show, there is not much of an alternative. Try this approach. If you are reaching these final lines after reading what preceded them, allow me to thank you for your patience, and to hope that this rather long chain of reflections on verification will have brought you some new insights into the fascinating challenge of writing correct programs.

References

[1] Nadia Polikarpova, Julian Tschannen, and Carlo A. Furia: A Fully Verified Container Library, in Proceedings of 20th International Symposium on Formal Methods (FM 15), 2015. (Best paper award.)

[2] Martin Nordio, Cristiano Calcagno, Peter Müller and Bertrand Meyer: A Sound and Complete Program Logic for Eiffel, in Proceedings of TOOLS 2009 (Technology of Object-Oriented Languages and Systems), Zurich, June-July 2009, eds. M. Oriol and B. Meyer, Springer LNBIP 33, June 2009.

[3] Boogie page at MSR, see here for publications and other information.

[4] Z3 was also originally from MSR and has been open-sourced, one can get access to publications and other information from  its Wikipedia page.

[5] Carlo Furia, Bertrand Meyer and Sergey Velder: Loop invariants: Analysis, Classification and Examples, in ACM Computing Surveys, vol. 46, no. 3, February 2014. Available here.

[6] Dynamic programming is a form of recursion removal, turning a recursive algorithm into an iterative one by using techniques known as “memoization” and  “bottom-up computation” (Berry). In this transformation, the invariant plays a key role. I will try to write this up some day as it is a truly elegant and illuminating explanation.

The “Morgenstern Colloquium” at the University of Nice / INRIA Sophia Antipolis invited me to give a talk, next Wednesday (18 December) at 11 in Sophia Antipolis, in the aptly named* “Kahn Building”. The announcement appears here. I proposed various topics but (pleasant surprise) the organizers explicitly asked me to lecture about what I really want to talk about: the Eiffel approach. I will give a general presentation describing not specifically the language but the unified view of software construction embodied in Eiffel, from modeling to requirements to design, implementation and verification. Here is the abstract:

With society’s growing reliance on IT systems, the ability to write high-quality software is ever more critical. While a posteriori verification techniques have their role, there is no substitute for methods and tools that provide built-in quality (“correctness by construction”) and scale up to very large systems. For several decades my colleagues and I have been building such a method, based in particular on the concept of Design by Contract, the associated tools and the supporting language, Eiffel. The scope is wide, encompassing all aspects of the software development process, from requirements and design to implementation and verification. I will present an overview of the approach, show what it can yield, and discuss remaining open issues.

This talk is meant for everyone, whether from industry or academia, with an interest in practical techniques for engineering high-quality software.

No registration is required. The presentation will be in English.

Note

*Gilles Kahn, a brilliant computer scientist who died too young, was for a while director of INRIA.

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.)

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).

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:

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:

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:

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:

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.

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:

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

A reminder about this year’s LASER school, taking place in Elba, Italy, June 1 to 9. The theme is

               AI + ML + SE

and the speakers:

• Shai Ben-David, University of Waterloo
• Lionel C. Briand, University of Luxembourg
• Pascal Fua, EPFL
• Eric Meijer, Facebook
• Tim Menzies, NC State University
• Me

Details at https://www.laser-foundation.org/school/.  From that page:

The 15th edition of the prestigious LASER summer school, in the first week of June 2019, will be devoted to the complementarity and confluence of three major areas of innovation in IT: Artificial Intelligence, Machine Learning and of course Software Engineering.

The school takes place in the outstanding environment of the Hotel del Golfo in Procchio, Elba, off the coast of Tuscany.

We “core” computer scientists and software engineers always whine that our research themes forever prevent us, to the delight of our physicist colleagues but unjustly, from reaching the gold standard of academic recognition: publishing in Nature. I think I have broken this barrier now by disproving the old, dusty laws of physics! Brace yourself for my momentous discovery: I have evidence of negative speeds.

My experimental setup (as a newly self-anointed natural scientist I am keen to offer the possibility of replication) is the Firefox browser. I was downloading an add-on, with a slow connection, and at some point got this in the project bar:

Negative speed! Questioning accepted wisdom! Nobel in sight! What next, cold fusion?

I fear I have to temper my enthusiasm in deference to more mundane explanations. There’s the conspiracy explanation: the speed is truly negative (more correctly, it is a “velocity”, a vector of arbitrary direction, hence in dimension 1 possibly negative); Firefox had just reversed the direction of transfer, surreptitiously dumping my disk drive to some spy agency’s server.

OK, that is rather far-fetched. More likely, it is a plain bug. A transfer speed cannot be negative; this property is not just wishful thinking but should be expressed as an integral part of the software. Maybe someone should tell Firefox programmers about class invariants.

(Reposted from the CACM blog [*].)

Software engineering was never a popular subject. It started out as “programming methodology”, evoking the image of bearded middle-aged men telling you with a Dutch, Swiss-German or Oxford accent to repent and mend your ways. Consumed (to paraphrase Mark Twain) by the haunting fear that someone, somewhere, might actually enjoy coding.

That was long ago. With a few exceptions including one mentioned below, to the extent that anyone still studies programming methodology, it’s in the agile world, where the decisive argument is often “I always say…”. (Example from a consultant’s page:  “I always tell teams: `I’d like a [user] story to be small, to fit in one iteration but that isn’t always the way.’“) Dijkstra did appeal to gut feeling but he backed it through strong conceptual arguments.

The field of software engineering, of which programming methodology is today just a small part, has enormously expanded in both depth and width. Conferences such as ICSE and ESEC still attract a good crowd, the journals are buzzing, the researchers are as enthusiastic as ever about their work, but… am I the only one to sense frustration? It is not clear that anyone outside of the community is interested. The world seems to view software engineering as something that everyone in IT knows because we all develop software or manage people who develop software. In the 2017 survey of CS faculty hiring in the U.S., software engineering accounted, in top-100 Ph.D.-granting universities, for 3% of hires! (In schools that stop at the master’s level, the figure is 6%; not insignificant, but not impressive either given that these institutions largely train future software engineers.) From an academic career perspective, the place to go is obviously  “Artificial Intelligence, Data Mining, and Machine Learning”, which in those top-100 universities got 23% of hires.

Nothing against our AI colleagues; I always felt “AI winter” was an over-reaction [1], and they are entitled to their spring. Does it mean software engineering now has to go into a winter of its own? That is crazy. Software engineering is more important than ever. The recent Atlantic  “software apocalypse” article (stronger on problems than solutions) is just the latest alarm-sounding survey. Or, for just one recent example, see the satellite loss in Russia [2] (juicy quote, which you can use the next time you teach a class about the challenges of software testing: this revealed a hidden problem in the algorithm, which was not uncovered in decades of successful launches of the Soyuz-Frigate bundle).

Such cases, by the way, illustrate what I would call the software professor’s dilemma, much more interesting in my opinion than the bizarre ethical brain-teasers (you see what I mean, trolley levers and the like) on which people in philosophy departments spend their days: is it ethical for a professor of software engineering, every morning upon waking up, to go to cnn.com in the hope that a major software-induced disaster has occurred,  finally legitimizing the profession? The answer is simple: no, that is not ethical. Still, if you have witnessed the actual state of ordinary software development, it is scary to think about (although not to wish for) all the catastrophes-in-waiting that you suspect are lying out there just waiting for the right circumstances .

So yes, software engineering is more relevant than ever, and so is programming methodology. (Personal disclosure: I think of myself as the very model of a modern methodologist [3], without a beard or a Dutch accent, but trying to carry, on today’s IT scene, the torch of the seminal work of the 1970s and 80s.)

What counts, though, is not what the world needs; it is what the world believes it needs. The world does not seem to think it needs much software engineering. Even when software causes a catastrophe, we see headlines for a day or two, and then nothing. Radio silence. I have argued to the point of nausea, including at least four times in this blog (five now), for a simple rule that would require a public auditing of any such event; to quote myself: airline transportation did not become safer by accident but by accidents. Such admonitions fall on deaf ears. As another sign of waning interest, many people including me learned much of what they understand of software engineering through the ACM Risks Forum, long a unique source of technical information on software troubles. The Forum still thrives, and still occasionally reports about software engineering issues, but most of the traffic is about privacy and security (with a particular fondness for libertarian rants against any reasonable privacy rule that the EU passes). Important topics indeed, but where do we go for in-depth information about what goes wrong with software?

Yet another case in point is the evolution of programming languages. Language creation is abuzz again with all kinds of fancy new entrants. I can think of one example (TypeScript) in which the driving force is a software engineering goal: making Web programs safer, more scalable and more manageable by bringing some discipline into the JavaScript world. But that is the exception. The arguments for many of the new languages tend to be how clever they are and what expressive new constructs they introduce. Great. We need new ideas. They would be even more convincing if they addressed the old, boring problems of software engineering: correctness, robustness, extendibility, reusability.

None of this makes software engineering less important, or diminishes in the least the passion of those of us who have devoted our careers to the field. But it is time to don our coats and hats: winter is upon us.

Notes

[1] AI was my first love, thanks to Jean-Claude Simon at Polytechnique/Paris VI and John McCarthy at Stanford.

[2] Thanks to Nikolay Shilov for alerting me to this information. The text is in Russian but running it through a Web translation engine (maybe this link will work) will give the essentials.

[3] This time borrowing a phrase from James Noble.

[*] I am reposting these CACM blog articles rather than just putting a link, even though as a software engineer I do not like copy-paste. This is my practice so far, and it might change since it raises obvious criticism, but here are the reasons: (A) The audiences for the two blogs are, as experience shows, largely disjoint. (B) I like this site to contain a record of all my blog articles, regardless of what happens to other sites. (C) I can use my preferred style conventions.

One of the most significant recent developments in software engineering is the concept of Devops*. Dismissing the idea as “just the latest buzzword” would be wrong. It may be a buzzword but it reflects a fundamental change in the way we structure system development; with web applications in particular the traditional distinctions between steps of development, V&V** and deployment fade out. If you are using Microsoft Word, you know or can easily find out the version number; but which version of your search engine are you using?

With the new flexibility indeed come new risks, as when a bug in the latest “devopsed”  version of Google Docs caused me to lose a whole set of complex diagrams irretrievably; an earlier article on this blog (“The Cloud and Its Risks“, October 2010) told the story.

In the new world of continuous integrated development/V&V/deployment, software engineering principles are more necessary than ever, but their application has to undergo a profound adaptation.

With Jean-Michel Bruel (Toulouse), Elisabetta Di Nitto (Milan) and Manuel Mazzara (Innopolis), we are organizing a workshop on the topic, DEVOPS 18, on 5-6 March 2018 near Toulouse. The Call for Papers is available here, with Springer LNCS proceedings. The submission deadline is January 15, but for that date a 2-page extended abstract is sufficient. I hope that the event will help the community get a better grasp of the software engineering techniques and practices applicable to this new world of software development.

Notes

*I know, it’s supposed to be DevOps (I am not a great fan of upper case in the middle of words).
** Validation & Verification.

As part of the continuation of the ERC Advanced Investigator Grant project “Concurrency Made Easy” (started at ETH Zurich, see the project pages at cme.ethz.ch), I have positions at Politecnico di Milano for:

• Postdocs (having a doctoral degree)
• Research associates (officially: “Assegno di Ricerca”, with the requirement of having a master degree), which can lead to a PhD position.

The deadline for applications is October 11. Please contact me directly if interested. What I expect:

• The requisite degrees as stated above.
• Innovative and enterprising spirit, passion for quality work in software engineering.
• Either or both of excellent programming abilities and strong CS theoretical background.
• Knowledge of as many of possible of: object-oriented programming, concurrency/parallelism, software verification/formal methods, Eiffel.
• Familiarity with the basics of the project as described in the project pages at the URL above.

The AutoProof technology pursues the goal of “Verification As a Matter Of Course”, integrated into the EVE development environment. (The AutoProof  project page here; see particularly the online interactive tutorial.) A one-day workshop devoted to the existing AutoProof and current development will take place on October 1 near Toulouse in France. It is an informal event (no proceedings planned at this point, although based on the submissions we might decide to produce a volume), on a small scale, designed to bring together people interested in making the idea of practical verification a reality.

The keynote will be given by Rustan Leino from Microsoft Research, the principal author of the Boogie framework on which the current implementation of AutoProof relies.

For submissions (or to attend without submitting) see the workshop page here. You are also welcome to contact me for more information.

A third ACM webinar this year (after two on agile methods): I will be providing a general introduction to Design by Contract. The date is this coming Thursday, September 17, and the time is noon New York (18 Paris/Zurich, 17 London, 9 Los Angeles, see here for hours elsewhere). Please tune in! The event is free but requires registration here.

Programming, wrote Dijkstra many years ago, is a branch of applied mathematics. That is only half of the picture: the other half is engineering, and this dual nature of programming is part of its attraction.

Descriptions of the mathematical side are generally, in my view, too complicated. This article [1] presents a mathematical theory of programs and programming based on concepts taught in high school: elementary set theory. The concepts covered include:

• Programming.
• Specification.
• Refinement.
• Non-determinism.
• Feasibility.
• Correctness.
• Programming languages.
• Kinds of programs: imperative, functional, object-oriented.
• Concurrency (small-step and large-step)
• Control structures (compound, if-then-else and Dijkstra-style conditional, loop).
• State, store and environment.
• Invariants.
• Notational conventions for building specifications and programs incrementally.
• Loop invariants and variants.

One of the principal ideas is that a program is simply the description of a mathematical relation. The program text is a rendering of that relation. As a consequence, one may construct programming languages simply as notations to express certain kinds of mathematics. This approach is the reverse of the usual one, where the program text and its programming languages are the starting point and the center of attention: theoreticians develop techniques to relate them to mathematical concepts. It is more effective to start from the mathematics (“unparsing” rather than parsing).

All the results (74 properties expressed formally, a number of others in the text) are derived as theorems from rules of elementary set theory; there are no new axioms whatsoever.

The paper also has a short version [2], omitting proofs and many details.

References

[1] Theory of Programs, available here.
[2] Theory of Programs, short version of [1] (meant for quick understanding of the ideas, not for publication), available here.

Opinions requested! See at end.

A void call, during the execution of an object-oriented program, is a call of the standard OO form

x·some_routine (…)                                                /CALL/

where x, a reference, happens to be void (null) instead of denoting, as expected, an object. The operation is not possible; it leads to an exception and, usually, a crash of the program. Void calls are also called “null pointer dereferencing”.

One of the major advances in Eiffel over the past years has been the introduction of attached types, entirely removing the risk of void calls. The language mechanisms, extending the type system, make void-call avoidance a static property, part of type checking: just as the compiler will prevent you from assigning a boolean value to an integer variable, so will it flag your program if it sees a risk of void call. Put the other way around, if your program passes compilation, you have the guarantee that its executions will never produce a void call. Attached types thus remove one of the major headaches of programming, what Tony Hoare [1] called his “one-billion-dollar mistake”:

I call it my billion-dollar mistake. It was the invention of the null reference in 1965. At that time, I was designing the first comprehensive type system for references in an object oriented language (ALGOL W) [2]. My goal was to ensure that all use of references should be absolutely safe, with checking performed automatically by the compiler. But I couldn’t resist the temptation to put in a null reference, simply because it was so easy to implement. This has led to innumerable errors, vulnerabilities, and system crashes, which have probably caused a billion dollars of pain and damage in the last forty year

Thanks to attached types, Eiffel programmers can sleep at night: their programs will not encounter void calls.

To benefit from this advance, you must declare variables accordingly, as either attached (never void after initialization) or detachable (possibly void). You must also write the program properly:

• If you declare x attached, you must ensure in the rest of the program that before its first use x will have been attached to an object, for example through a creation instruction create x.
• If you declare x detachable, you must make sure that any call of the above form /CALL/ happens in a context where x is guaranteed to be non-void; for example, you could protect it by a test if x /= Void then… or, better, an “object test”.

Code satisfying these properties is called void-safe.

Void safety is the way to go: who wants to worry about programs, even after they have been thoroughly tested and have seemingly worked for a while, crashing at unpredictable times? The absence of null-pointer-dereferencing can be a statically  enforced property, as the experience of Eiffel now demonstrates; and that what it should be. One day, children will think void-safely from the most tender age, and their great-grandparents will tell them, around the fireplace during long and scary winter nights, about the old days when not everyone was programming in Eiffel and even those who did were worried about the sudden null-pointer-derefencing syndrome. To get void safety through ordinary x: PERSON declarations, you had (children, hold your breath) to turn on a compiler option!

The transition to void safety was neither fast nor easy; in fact, it has taken almost ten years. Not everyone was convinced from the beginning, and we have had to improve and simplify the mechanism along the way to make void-safe programming practical. Compatibility has been a key issue throughout: older classes are generally not void-safe, but in a language that has been around for many years and has a large code base of operational software it is essential to ensure a smooth transition. Void safety has, from its introduction, been controlled by a compiler option:

• With the option off, old code will compile as it used to do, but you do not get any guarantee of void safety. At execution time, a void call can still cause your program to go berserk.
• With the option on, you get the guarantee: no void calls. To achieve this goal, you have to make sure the classes obey the void safety rules; if they do not, the compiler will reject them until you fix the problem.

In the effort to reconcile the compatibility imperative with the inexorable evolution to void safety, the key decisions have affected default values for compiler options and language conventions. Three separate decisions, in fact. Two of the defaults have already been switched; the question asked at the end of this article addresses the switching of the last remaining one.

The first default governed the void-safety compiler option. On its introduction, void-safety was off by default; the mechanism had to be turned on explicitly, part of the “experimental” option that most EiffelStudio releases offer for new, tentative mechanisms. That particular decision changed a year ago, with version 7.3 (May 2013): now void safety is the default. To include non-void-safe code you must mark  it explicitly.

The second default affects a language convention: the meaning of a standard declaration. A typical declaration, such as

x: PERSON                                                                                      /A/

says that at run time x denotes a reference which, if not void, will be attached to an object of type PERSON.  In pre-void-safety Eiffel, as in today’s other typed OO languages,  the reference could occasionally become void at run time; in other words, x was detachable. With the introduction of void safety, you could emphasize this property by specifying it explicitly:

x: detachable PERSON                                                             /B/

You could also specify that x would never be void by declaring it attached, asking the compiler to guarantee this property for you (through its application of the void-safety rules to all operations involving x). The explicit form in this case is

x: attached PERSON                                                               /C/

In practical programming, of course, you do not want to specify attached or detachable all the time: you want to use the simple form /A/ as often as possible. Originally, since we were starting from a non-void-safe language, compatibility required /A/ to mean /B/ by default. But it turns out that “attached” really is the dominant case: most references should remain attached at all times and Void values should be reserved for important but highly specialized cases such as terminating linked data structures. So the simple form should, in the final state of the language, mean /C/. That particular default was indeed switched early (version 7.0, November 2011) for people using the void-safety compiler option. As a result, the attached keyword is no longer necessary for declarations such as the above, although it remains available. Everything is attached by default; when you want a reference that could be void (and are prepared to bear the responsibility for convincing the compiler that it won’t when you actually use it in a call), you declare it as detachable; that keyword remains necessary.

There remains one last step in the march to all-aboard-for-void-safety: removing the “detachable by default” option, that is to say, the compiler option that will make /A/ mean /B/ (rather than /C/). It is only an option, and not the default; but still it remains available. Do we truly need it? The argument for removing it  is that it simplifies the specification (the fewer options the better) and encourages everyone, even more than before, to move to the new world. The argument against is to avoid disturbing existing projects, including their compiler control files (ECFs).

The question looms: when do we switch the defaults? Some of us think the time is now; specifically, the November release (14.11) [4].

Do you think the option should go? We would like your opinion. Please participate in the Eiffelroom poll [5].

References and note

[1] C.A.R. Hoare: Null References: The Billion Dollar Mistake , abstract of talk at QCon London, 9-12 March 2009, available here.

[2] (BM note) As a consolation, before Algol W, LISP already had NIL, which is the null pointer.

[3] Bertrand Meyer, Alexander Kogtenkov and Emmanuel Stapf: Avoid a Void: The Eradication of Null Dereferencing, in Reflections on the Work of C.A.R. Hoare, eds. C. B. Jones, A.W. Roscoe and K.R. Wood, Springer-Verlag, 2010, pages 189-211, available here.

[4] EiffelStudio version numbering changed in 2014: from a classic major_number.minor_number to a plain year.month, with two principal releases, 5 and 11 (May and November).

[5] Poll on switching the attachment defaults: at the bottom of the Eiffelroom page here (direct access here).

(Adapted from an article previously published on the CACM blog.)

Often, you will be told that programming languages do not matter much. What actually matters more is not clear; maybe tools, maybe methodology, maybe process. It is a pretty general rule that people arguing that language does not matter are defending bad languages.

Let us consider the Apple bug of a few weeks ago. Only a few weeks; the world has already moved to Heartbleed (to be discussed in a subsequent article), but that is not a reason to sweep away the memory of the Apple bug and the language design that it reflects.

In late February, users of  iPhones, iPads and iPods were enjoined to upgrade their devices immediately because  “an attacker with a privileged network position may capture or modify data in sessions protected by SSL/TLS.” The bug was traced [1] to code of the following form:

if (error_of_first_kind)
goto fail;
if (error_of_second_kind)
goto fail;
if (error_of_third_kind)
goto fail;
if (error_of_fourth_kind)
goto fail;
if (error_of_fifth_kind)
goto fail;
goto fail;
if (error_of_sixth_kind)
goto fail;
The_truly_important_code_handling_non_erroneous_case

In other words: just a duplicated line! (The extra line is highlighted above.) But the excess “goto” is beyond the scope of the preceding “if“, so it is executed unconditionally: all executions go directly to the “fail” label, so that The_truly_important_code_handling_non_erroneous_case never gets executed.

Critics have focused their ire on the  goto instruction, but it is of little relevance. What matters, language-wise, is the C/C++-Java-C# convention of delimiting the scope of conditional instructions, loops and other kinds of composite structures. Every component of such structures in these languages is syntactically a single instruction, so that:

• If you want the branch to consist of an atomic instruction, you write that instruction by itself, as in: if (c) a = b;
• If you want a sequence of instructions, you write it as a compound, enclosed by the ever so beautiful braces: if (c) {a = b; x = y;}

Although elegant in principle (after all, it comes from Algol), this convention is disastrous from a software engineering perspective because software engineering means understanding that programs change. One day, a branch of a conditional or loop has one atomic instruction; sometime later, a maintainer realizes that the corresponding case requires more sophisticated treatment, and adds an instruction, but fails to add the braces.

The proper language solution is to do away with the notion of compound instruction as a separate concept, but simply expect all branches of composite instructions to consist of a sequence, which could consist of several instructions, just one, or none at all. In Eiffel, you will write

if  c then
   x := y
end

or

 if  c then
   a := b
   x := y
else
   u := v
end

or

from i := 1 until c loop
   a := b
   i := i + 1
end

or

across my_list as l loop
   l.add (x)
end

and so on. This syntax also gets rid of all the noise that pollutes programs in languages retaining C’s nineteen-sixties conventions: parentheses around the conditions, semicolons for instructions on different lines; these small distractions accumulate into serious impediments to program readability.

With such a modern language design, the Apple bug could not have arisen. A duplicated line is either:

• A keyword such as end, immediately caught as a syntax error.
• An actual instruction such as an assignment, whose duplication causes either no effect or an effect limited to the particular case covered by the branch, rather than catastrophically disrupting all cases, as in the Apple bug.

Some people, however, find it hard to accept the obvious responsibility of language design. Take this comment derisively entitled  “the goto squirrel” by Dennis Hamilton in the ACM Risks forum [2]:

It is amazing to me that, once the specific defect is disclosed (and the diff of the actual change has also been published), the discussion has devolved into one of coding style and whose code is better.  I remember similar distractions around the Ariane 501 defect too, although in that case there was nothing wrong with the code—the error was that it was being run when it wasn’t needed and it was not simulation tested with new launch parameters under the mistaken assumption that if the code worked for Ariane 4, it should work for Ariane 5.

It is not about the code.  It is not about the code.  It is not about goto. It is not about coming up with ways to avoid introducing this particular defect by writing the code differently.

Such certainty! Repeating a wrong statement ( “it is not about the code“) does not make it  right. Of course “it” is about the code! If the code had been different the catastrophe would not have happened, so one needs some gall to state that the code is not the issue — and just as much gall, given that the catastrophe would also not have happened if the programming language had been different, to state that it is not about the programming language.

When Mr. Hamilton dismisses as “distractions” the explanations pointing to programming-related causes for the Ariane-5 disaster, I assume he has in mind the analysis which I published at the time with Jean-Marc Jézéquel [3], which explained in detail how the core issue was the absence of proper specifications (contracts). At that time too, we heard dismissive comments; according to one of the critics, the programming aspects did not count, since the whole thing was really a social problem: the French engineers in Toulouse did not communicate properly with their colleagues in England! What is great with such folk explanations is that they sound just right and please people because they reinforce existing stereotypes. They are by nature as impossible to refute as they are impossible to prove. And they avoid raising the important but disturbing questions: were the teams using the right programming language, the right specification method (contracts, as our article suggested), appropriate tools? In both the Ariane-5 and Apple cases, they were not.

If you want to be considered polite, you are not supposed to point out that the use of programming languages designed for the PDP-8 or some other long-gone machine is an invitation to disaster. The more terrible the programming language people use, and the more they know it is terrible (even if they will not admit it), the more scandalized they will be that you point out that it is, indeed, terrible. It is as if you had said something about their weight or the pimples on their cheeks. Such reactions do not make the comment less true. The expression of outrage is particularly inappropriate when technical choices are not just matters for technical argument, but have catastrophic consequences on society.

The usual excuse, in response to language criticisms, is that better tools, better quality control (the main recommendation of the Ariane-5 inquiry committee back in 1997), better methodology would also have avoided the problem. Indeed, a number of the other comments in the comp.risks discussion that includes Hamilton’s dismissal of code [2] point in this direction, noting for example that static analyzers could have detected code duplication and unreachable instructions. These observations are all true, but change nothing to the role of programming languages and coding issues.  One of the basic lessons from the study of software and other industrial disasters — see for example the work of Nancy Leveson — is that a disaster results from a combination of causes. This property is in fact easy to understand: a disaster coming from a single cause would most likely have been avoided. Consider the hypothetical example of a disastrous flaw in Amazon’s transaction processing. It seems from various sources that Amazon processes something like 300 transactions a second. Now let us assume three independent factors, each occurring with a probability of a thousandth (10^-3), which could contribute to a failure. Then:

• It is impossible that one of the factors could cause failure just by itself: that means it would make a transaction fail after around 3 seconds, and would be caught even in the most trivial unit testing. No one but the developer would ever know about it.
• If two of the factors together cause failure, they will occur every million transactions, meaning about once an hour. Any reasonable testing will discover the problem before a release is ever deployed.
• If all three factors are required, the probability is 10^-9, meaning that a failure will occur about once a year. Only in that case will a real problem exist: a flaw that goes undetected for a long time, during which everything seems normal, until disaster strikes.

These observations explain why post-mortem examinations of catastrophes always point to a seemingly impossible combination of unfortunate circumstances. The archduke went to Sarajevo and he insisted on seeing the wounded and someone forgot to tell the drivers about the prudent decision to bypass the announced itinerary and the convoy stalled  and the assassin saw it and he hit Franz-Ferdinand right in the neck and there was nationalistic resentment in various countries and the system of alliances required countries to declare war [4]. Same thing for industrial accidents. Same thing for the Apple bug: obviously, there were no good code reviews and no static analysis tools applied and no good management; and, obviously, a programming language that blows out innocent mistakes into disasters of planetary import.

So much for the accepted wisdom, heard again and again in software engineering circles, that code does not matter, syntax does not count, typos are caught right away, and that all we should care about is process or agility or requirements or some other high-sounding concern more respectable than programming. Code? Programming languages? Did we not take care of those years ago? “I remember similar distractions.”

There is a  positive conclusion to the “and” nature (in probabilistic terms, the multiplicative nature) of causes necessary to produce a catastrophe in practice: it suffices to get rid of one of the operands of the “and” to falsify its result, hence avoiding the catastrophe. When people tell you that code does not matter or that language does not matter, just understand the comment for what it really means, “I am ashamed of the programming language and techniques I use but do not want to admit it so I prefer to blame problems on the rest of the world“, and make the correct deduction: use a good programming language.

References

[1] Paul Duckline:  Anatomy of a “goto fail” – Apple’s SSL bug explained, plus an unofficial patch for OS X!, Naked Security blog (Sophos), 24 February 2014, available here.

[2] Dennis E. Hamilton: The Goto Squirrel, ACM Risks Forum, 28 February 2014, available here.

[3] Jean-Marc Jézéquel and Bertrand Meyer: Design by Contract: The Lessons of Ariane, in Computer (IEEE), vol. 30, no. 1, January 1997, pages 129-130, available online here and, with reader responses here.

[4] Assassination of Ferdinand of Autria: here.

For almost anyone programming in Eiffel, contracts are just a standard part of daily life; Patrice Chalin’s pioneering study of a few years ago [1] confirmed this impression. A larger empirical study is now available to understand how developers actually use contracts when available. The study, to published at FM 2014 [2] covers 21 programs, not just in Eiffel but also in JML and in Code Contracts for C#, totaling 830,000 lines of code, and following the program’s revision history for a grand total of 260 million lines of code over 7700 revisions. It analyzes in detail whether programmers use contracts, how they use them (in particular, which kinds, among preconditions, postconditions and invariants), how contracts evolve over time, and how inheritance interacts with contracts.

The paper is easy to read so I will refer you to it for the detailed conclusions, but one thing is clear: anyone who thinks contracts are for special development or special developers is completely off-track. In an environment supporting contracts, especially as a native part of the language, programmers understand their benefits and apply them as a matter of course.

References

[1] Patrice Chalin: Are practitioners writing contracts?, in Fault-Tolerant System, eds. Butler, Jones, Romanovsky, Troubitsyna, Springer LNCS, vol. 4157, pp. 100–113, 2006.

[2] H.-Christian Estler, Carlo A. Furia, Martin Nordio, Marco Piccioni and Bertrand Meyer: Contracts in Practice, to appear in proceedings of 19th International Symposium on Formal Methods (FM 2014), Singapore, May 2014, draft available here.

As part of our “Concurrency Made Easy” ERC Advanced Investigator Grant project (2012-2017), we are offering PhD positions at the Chair of Software Engineering of ETH Zurich. The goal of the project is to build a sophisticated programming and verification architecture to make concurrent and distributed programming simple and reliable, based on the ideas of Eiffel and particularly the SCOOP concurrency model. Concurrency in its various forms (particularly multithreading) as well as distributed computing are required for most of today’s serious programs, but programming concurrent applications remains a challenge. The CME project is determined to break this complexity barrier.  Inevitably, achieving simplicity for users (in this case, application programmers) requires, under the hood, a sophisticated infrastructure, both conceptual (theoretical models) and practical (the implementation). We are building that infrastructure.

ETH offers an outstanding research and education environment and competitive salaries for “assistants” (PhD students), who are generally expected in addition to their research to participate in teaching, in particular introductory programming, and other activities of the Chair.  The candidates we seek have: a master’s degree in computer science or related field from a recognized institution (as required by ETH); a strong software engineering background, both practical and theoretical, and more generally a strong computer science and mathematical culture; a good knowledge of verification techniques (e.g. Hoare-style, model-checking, abstract interpretation); some background in concurrency or distribution; and a passion for high-quality software development. Prior publications, and experience with Eiffel, are pluses. In line with ETH policy, particular attention will be given to female candidates.

Before applying, you should become familiar with our work; see in particular the research pages at se.ethz.ch including the full description of the CME project at cme.ethz.ch.

Candidates should send (in PDF or text ) to se-open-positions@lists.inf.ethz.ch a CV and a short cover letter describing their view of the CME project and ideas about their possible contribution.

I have mentioned this paper before (see the earlier blog entry here) but it is now going to be published [1] and has been significantly revised, both to take referee comments into account and because we found better ways to present the concepts.

We have  endeavored to explain better than in the draft why the concept of negative variable is necessary and why the usual techniques for modeling object-oriented programs do not work properly for the fundamental OO operation, qualified call x.r (…). These techniques are based on substitution and are simply unable to express certain properties (let alone verify them). The affected properties are those involving properties of the calling context or the global project structure.

The basic idea (repeated in part from the earlier post) is as follows. In modeling OO programs, we have to take into account the unique “general relativity” property of OO programming: all the operations you write are expressed relative to a “current object” which changes repeatedly during execution. More precisely at the start of a call x.r (…) and for the duration of that call the current object changes to whatever x denotes — but to determine that object we must again interpret x in the context of the previous current object. This raises a challenge for reasoning about programs; for example in a routine the notation f.some_reference, if f is a formal argument, refers to objects in the context of the calling object, and we cannot apply standard rules of substitution as in the non-OO style of handling calls.

We introduced a notion of negative variable to deal with this issue. During the execution of a call x.r (…) the negation of x , written x’, represents a back pointer to the calling object; negative variables are characterized by axiomatic properties such as x.x’= Current and x’.(old x)= Current.

The paper explains why this concept is necessary, describes the associated formal rules, and presents applications.

Reference

[1] Bertrand Meyer and Alexander Kogtenkov: Negative Variables and the Essence of Object-Oriented Programming, to appear in Specification, Algebra, and Software, eds. Shusaku Iida, Jose Meseguer and Kazuhiro Ogata, Springer Lecture Notes in Computer Science, 2014, to appear. See text here.

There will be two talks in the Software Engineering Seminar at ITMO, 18:00 local time, Tuesday, January 14, 2014. Please arrive 10 minutes early for registration.

Place: ITMO, Sytninskaya Ulitsa, Saint Petersburg.

Andrey Terekhov (SPBGU): Programming crystals

(I do not know whether this talk will be in Russian or English. An abstract follows but the talk is meant as the start of a discussion rather than a formal lecture.)

В течение последних 20-30 лет основными языками программирования кристаллов были VHDL и Verilog. Эти языки изначально проектировались как средства создания проектной документации, потом они стали использоваться в качестве инструмента моделирования и только сравнительно недавно для этих языков появились средства генерации кода уровня RTL (Register Transfer Language). Тексты на  VHDL и Verilog очень громоздки, трудно читаемые, плохо стандартизованы (одна и та же программа может синтезироваться на одном инструменте и не поддаваться синтезу на другом. Лет 10 назад появился язык SystemC – это С++ с огромным набором библиотек. С одной стороны, любая программа на SystemC может транслироваться стандартными трансляторами С++ , есть удобные средства потактного моделирования и приличные средства генгерации RTL, с другой стороны, требование совместимости с С++ не прошло даром – если в базовом языке нет средств описания параллелизма и конвейеризации, их приходится добавлять весьма искусственными приемами через приставные библиотеки. Буквально в прошлом году фирма Xilinx выпустила продукт Vivado, в рекламе которого утверждается, что он способен автоматически транслировать обычные программы на С/C++ в RTL промышленного качества.

Мы выполнили несколько экспериментов по использованию этого продукта, оказалось, что обещанной автоматизации там нет, пользователь должен писать на С, постоянно думая о том, как его код будет выглядеть в финальном RTL,  расставлять огромное количество прагм, причем не всегда очевидных.

Основной тезис доклада – такая важная область, как проектирование кристаллов, нуждается в специализированных языковых и инструментальных средствах, обеспечивающих  создание компактных и  легко читаемых программ, которые могут быть использованы как для симуляции, так и для генерации эффективного RTL. В докладе будут приведены примеры программ на языке HaSCoL (Hardware and Software Codesign Language), разработанном на кафедре системного программирования СПбГУ, и даны некоторые сравнительные характеристики.

Sergey Velder (ITMO): Alias graphs

(My summary – BM.) In the ITMO SEL work on automatic alias analysis, a new model has been developed: alias graphs, an abstraction of the object structure. This short talk will compare it to previously used approaches.

For a while now I have  been engaged in  a core problem of software verification: the aliasing problem. As with many difficult problems in science, it is easy to state the basic question: can we determine automatically whether at a program point p the values of two reference expressions e and f can ever denote the same object?

Alias analysis lies at the core of many problems in software analysis and verification.

Earlier work [2] I introduced an “alias calculus”. The calculus is a set of rules, attached to the constructs of the programming language, to compute the “alias relation”: the set of possibly aliased expression pairs. A new paper [1] with Sergey Velder and Alexander Kogtenkov improves the model (correcting in particular an error in the axiom for assignment, whose new version has been proved sound using Coq) and applies it to the inference of frame properties. Here the abstract:

Alias analysis, which determines whether two expressions in a program may reference to the same object, has many potential applications in program construction and verification. We have developed a theory for alias analysis, the “alias calculus”, implemented its application to an object-oriented language, and integrated the result into a modern IDE. The calculus has a higher level of precision than many existing alias analysis techniques. One of the principal applications is to allow automatic change analysis, which leads to inferring “modifies clauses”, providing a significant advance towards addressing the Frame Problem. Experiments were able to infer the “modifies” clauses of an existing formally specied library. Other applications, in particular to concurrent programming, also appear possible. The article presents the calculus, the application to frame inference including experimental results, and other projected applications. The ongoing work includes building more efficient model capturing aliasing properties and soundness proof for its essential elements.

This is not the end of the work, as better models and implementations are needed, but an important step.

References

[1] Sergey Velder, Alexander Kogtenkovand Bertrand Meyer: Alias Calculus, Frame Calculus and Frame Inference, in Science of Computer Programming, to appear in 2014 (appeared online 26 November 2013); draft available here, published version here.
[2] Bertrand Meyer: Steps Towards a Theory and Calculus of Aliasing, in International Journal of Software and Informatics, Chinese Academy of Sciences, 2011, pages 77-116, available here.

Yesterday, wanting to find out the platform of an arriving  train (stations are good at displaying departures, but don’t seem to consider arrival information worth showing), I fired up the “SBB Business” mobile application of the Swiss railways which I purchased some time ago:

The results are impressive: one can, they tell us, ride from Paris to Zurich — about 500 kilometers or 300 miles — in 56 minutes by leaving at 17:02. Wow! No wonder the entry displays (on the right) the graphical symbol for the highest possible expected passenger load, in both first and second class. With such a speed I would flock to that train too!

Nonsense of course. The TGV is fast, at least in the French part (from Basel to Zurich they seem to make it as slow as possible to prove some point), but it still takes four hours and three minutes. I have no idea where the program got the information it displays.

Trying to tap the “earlier” or “later” buttons does not help much, since what you get (consistently repeated if you keep trying, and confirmed again one day later) is this screen:

No clue what “F1” means.

Whatever software solutions the SBB uses, I am not impressed. Of course, they are welcome to ask for my suggestions.

I have mentioned this paper before but as a draft. It has now been accepted by ACM’s Computing Surveys and is scheduled to appear in September 2014; the current text, revised from the previous version, is available [1].

Here is the abstract:

Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a “loop invariant”. Beyond their role in verification, loop invariants help program understanding by providing fundamental insights into the nature of algorithms. In practice, finding sound and useful invariants remains a challenge. Fortunately, many invariants seem intuitively to exhibit a common flavor. Understanding these fundamental invariant patterns could therefore provide help for understanding and verifying a large variety of programs.

We performed a systematic identification, validation, and classification of loop invariants over a range of fundamental algorithms from diverse areas of computer science. This article analyzes the patterns, as uncovered in this study,governing how invariants are derived from postconditions;it proposes a taxonomy of invariants according to these patterns, and presents its application to the algorithms reviewed. The discussion also shows the need for high-level specifications based on “domain theory”. It describes how the invariants and the corresponding algorithms have been mechanically verified using an automated program prover; the proof source files are available. The contributions also include suggestions for invariant inference and for model-based specification.

Reference

[1] Carlo Furia, Bertrand Meyer and Sergey Velder: Loop invariants: Analysis, Classification and Examples, in ACM Computing Surveys, to appear in September 2014, preliminary text available here.

This report continues the series of ICSE 2013 article previews (see the posts of these last few days, other than the DOSE announcement), but is different from its predecessors since it talks about a paper from our group at ETH, so you should not expect any dangerously delusional,  disingenuously dubious or downright deceptive declaration or display of dispassionate, disinterested, disengaged describer’s detachment.

The paper [1] (mentioned on this blog some time ago) is entitled How good are software specifications? and will be presented on Wednesday by Nadia Polikarpova. The basic result: stronger specifications, which capture a more complete part of program functionality, cause only a modest increase in specification effort, but the benefits are huge; in particular, automatic testing finds twice as many faults (“bugs” as recently reviewed papers call them).

Strong specifications are specifications that go beyond simple contracts. A straightforward example is a specification of a push operation for stacks; in EiffelBase, the basic Eiffel data structure library, the contract’s postcondition will read

item = x                                          /A/
count = old count + 1

where x is the element being pushed, item the top of the stack and count the number of elements. It is of course sound, since it states that the element just pushed is now the new top of the stack, and that there is one more element; but it is also  incomplete since it says nothing about the other elements remaining as they were; an implementation could satisfy the contract and mess up with these elements. Using “complete” or “strong” preconditions, we associate with the underlying domain a theory [2], or “model”, represented by a specification-only feature in the class, model, denoting a sequence of elements; then it suffices (with the convention that the top is the first element of the model sequence, and that “+” denotes concatenation of sequences) to use the postcondition

model = <x> + old model         /B/

which says all there is to say and implies the original postconditions /A/.

Clearly, the strong contracts, in the  /B/ style, are more expressive [3, 4], but they also require more specification effort. Are they worth the trouble?

The paper explores this question empirically, and the answer, at least according to the criteria used in the study, is yes.  The work takes advantage of AutoTest [5], an automatic testing framework which relies on the contracts already present in the software to serve as test oracles, and generates test cases automatically. AutoTest was applied to both to the classic EiffelBase, with classic partial contracts in the /A/ style, and to the more recent EiffelBase+ library, with strong contracts in the /B/ style. AutoTest is for Eiffel programs; to check for any language-specificity in the results the work also included testing a smaller set of classes from a C# library, DSA, for which a student developed a version (DSA+) equipped with strong model-based contracts. In that case the testing tool was Microsoft Research’s Pex [7]. The results are similar for both languages: citing from the paper, “the fault rates are comparable in the C# experiments, respectively 6 . 10^-3 and 3 . 10^-3 . The fault complexity is also qualitatively similar.”

The verdict on the effect of strong specifications as captured by automated testing is clear: the same automatic testing tools applied to the versions with strong contracts yield twice as many real faults. The term “real fault” comes from excluding spurious cases, such as specification faults (wrong specification, right implementation), which are a phenomenon worth studying but should not count as a benefit of the strong specification approach. The paper contains a detailed analysis of the various kinds of faults and the corresponding empirically determined measures. This particular analysis is for the Eiffel code, since in the C#/Pex case “it was not possible to get an evaluation of the faults by the original developers“.

In our experience the strong specifications are not that much harder to write. The paper contains a precise measure: about five person-weeks to create EiffelBase+, yielding an “overall benefit/effort ratio of about four defects detected per person-day“. Such a benefit more than justifies the effort. More study of that effort is needed, however, because the “person” in the person-weeks was not just an ordinary programmer. True, Eiffel experience has shown that most programmers quickly get the notion of contract and start applying it; as the saying goes in the community, “if you can write an if-then-else, you can write a contract”. But we do not yet have significant evidence of whether that observation extends to model-based contracts.

Model-based contracts (I prefer to call them “theory-based” because “model” means so many other things, but I do not think I will win that particular battle) are, in my opinion, a required component of the march towards program verification. They are the right compromise between simple contracts, which have proved to be attractive to many practicing programmers but suffer from incompleteness, and full formal specification à la Z, which say everything but require too much machinery. They are not an all-or-nothing specification technique but a progressive one: programmers can start with simple contracts, then extend and refine them as desired to yield exactly the right amount of precision and completeness appropriate in any particular context. The article shows that the benefits are well worth the incremental effort.

According to the ICSE program the talk will be presented in the formal specification session, Wednesday, May 22, 13:30-15:30, Grand Ballroom C.

References

[1] Nadia Polikarpova, Carlo A. Furia, Yu Pei, Yi Wei and Bertrand Meyer: What Good Are Strong Specifications?, to appear in ICSE 2013 (Proceedings of 35th International Conference on Software Engineering), San Francisco, May 2013, draft available here.

[2] Bertrand Meyer: Domain Theory: the forgotten step in program verification, article on this blog, see here.

[3] Bernd Schoeller, Tobias Widmer and Bertrand Meyer: Making Specifications Complete Through Models, in Architecting Systems with Trustworthy Components, eds. Ralf Reussner, Judith Stafford and Clemens Szyperski, Lecture Notes in Computer Science, Springer-Verlag, 2006, available here.

[4] Nadia Polikarpova, Carlo Furia and Bertrand Meyer: Specifying Reusable Components, in Verified Software: Theories, Tools, Experiments (VSTTE ‘ 10), Edinburgh, UK, 16-19 August 2010, Lecture Notes in Computer Science, Springer Verlag, 2010, available here.

[5] Bertrand Meyer, Ilinca Ciupa, Andreas Leitner, Arno Fiva, Yi Wei and Emmanuel Stapf: Programs that Test Themselves, IEEE Computer, vol. 42, no. 9, pages 46-55, September 2009, also available here.

[6] Bertrand Meyer, Ilinca Ciupa, Andreas Leitner, Arno Fiva, Yi Wei and Emmanuel Stapf: Programs that Test Themselves, in IEEE Computer, vol. 42, no. 9, pages 46-55, September 2009, also available here.

[7] Nikolai Tillman and Peli de Halleux, Pex: White-Box Generation for .NET, in Tests And Proofs (TAP 2008), pp. 134-153.

(Please note the general disclaimer [1].)

How Misclassification Impacts Bug Prediction [2], an article to be presented on Thursday at ICSE, is the archetype of today’s successful empirical software engineering research, deriving significant results from the mining of publicly available software project repositories — in this case Tomcat5 and three others from Apache, as well as Rhino from Mozilla. The results are in some sense meta-results, because many studies have already mined the bug records of such repositories to draw general lessons about bugs in software development; what Herzig, Just and Zeller now tell us is that the mined data is highly questionable: many problems classified as bugs are not bugs.

The most striking results (announced in a style a bit stentorian to my taste, but indeed striking) are that: every third bug report does not describe a bug, but a request for a new feature, an improvement, better documentation or tests, code cleanup or refactoring; and that out of five program files marked as defective, two do not in fact contain any bug.

These are both false positive results. The repositories signal very few misclassifications the other way: only a small subset of enhancement and improvement requests (around 5%) should have been classified as bugs, and even fewer faulty files are missed (8%, but in fact less than 1% if one excludes an outlier, tomcat5 with 38%, a discrepancy that the paper does not discuss).

The authors have a field day, in the light of this analysis, of questioning the validity of the many studies in recent years — including some, courageously cited, by Zeller himself and coauthors — that start from bug repositories to derive general lessons about bugs and their properties.

The methodology is interesting if a bit scary. The authors (actually, just the two non-tenured authors, probably just a coincidence) analyzed 7401 issue reports manually; more precisely, one of them analyzed all of them and the second one took a second look at the reports that came out from the first step as misclassified, without knowing what the proposed reclassification was, then the results were merged. At 4 minutes per report this truly stakhanovite effort took 90 working days. I sympathize, but I wonder what the rules are in Saarland for experiments involving living beings, particularly graduate students.

Precise criteria were used for the reclassification; for example a report describes a bug, in the authors’ view, if it mentions a null pointer exception (I will skip the opportunity of a pitch for Eiffel’s void safety mechanism), says that the code has to be corrected to fix the semantics, or if there is a “memory issue” or infinite loop. These criteria are reasonable if a bit puzzling (why null pointer exceptions and not other crashes such as arithmetic overflows?); but more worryingly there is no justification for them. I wonder  how much of the huge discrepancy found by the authors — a third or reported bugs are not bugs, and 40% of supposedly defective program files are not defective — can be simply explained by different classification criteria applied by the software projects under examination. The authors give no indication that they interacted with the people in charge of these projects. To me this is the major question hovering over this paper and its spectacular results. If you are in the room and get the chance, don’t hesitate to ask this question on my behalf or yours!

Another obvious question is how much the results depend on the five projects selected. If there ever was room for replicating a study (a practice whose rarity in software engineering we lament, but whose growth prospects are limited by the near-impossibility of convincing selective software engineering venues to publish confirmatory empirical studies), this would be it. In particular it would be good to see some of the results for commercial products.

The article offers an explanation for the phenomena it uncovered: in its view, the reason why so many bug reports end up misclassified is the difference of perspective between users of the software, who complain about the problems they encounter,  and the software professionals  who prepare the actual bug reports. The explanation is plausible but I was surprised not to see any concrete evidence that supports it. It is also surprising that the referees did not ask the authors to provide more solid arguments to buttress that explanation. Yet another opportunity to raise your hand and ask a question.

This (impressive) paper will call everyone’s attention to the critical problem of data quality in empirical studies. It is very professionally prepared, and could, in addition to its specific contributions, serve as a guide on how to get an empirical software engineering paper accepted at ICSE: take a critical look at an important research area; study it from a viewpoint that has not been considered much so far; perform an extensive study, with reasonable methodological assumptions; derive a couple of striking results, making sure they are both visibly stated and backed by the evidence; and include exactly one boxplot.

Notes and references

[1] This article review is part of the “Reading Notes” series. General disclaimer here.

[2] Kim Herzig, Sascha Just and Andreas Zeller: It’s not a Bug, it’s a Feature: How Misclassification Impacts Bug Prediction, in ICSE 2013, available here. According to the ICSE program the paper will be presented on May 23 in the Bug Prediction session, 16 to 17:30.

To inaugurate the “Reading Notes” series [1] I will take articles from the forthcoming International Conference on Software Engineering. Since I am not going to ICSE this year I am instead spending a little time browsing through the papers, obligingly available on the conference site. I’ll try whenever possible to describe a paper before it is presented at the conference, to alert readers to interesting sessions. I hope in July and August to be able to do the same for some of the papers to be presented at ESEC/FSE [2].

Please note the general disclaimer [1].

The Design of Bug Fixes [3] caught my attention partly for selfish reasons, since we are working, through the AutoFix project [3], on automatic bug fixing, but also out of sheer interest and because I have seen previous work by some of the authors. There have been article about bug patterns before, but not so much is known with credible empirical evidence about bug fixes (corrections of faults). When a programmer encounters a fault, what strategies does he use to correct it? Does he always produce the best fix he can, and if so, why not? What is the influence of the project phase on such decisions (e.g. will you fix a bug the same way early in the process and close to shipping)? These are some of the questions addressed by the paper.

The most interesting concrete result is a list of properties of bug fixes, classified along two criteria: nature of a fix (the paper calls it “design space”), and reasoning behind the choice of a fix. Here are a few examples of the “nature” classification:

• Data propagation: the bug arises in a component, fix it in another, for example a library class.
• More or less accuracy: are we fixing the symptom or the cause?
• Behavioral alternatives: rather than directly correcting the reported problem, change the user-experienced behavior (evoking the famous quip that “it’s not a bug, it’s a feature”). The authors were surprised to see that developers (belying their geek image) seem to devote a lot of effort trying to understand how users actually use the products, but also found that even so developers do not necessarily gain a solid, objective understanding of these usage patterns. It would be interesting to know if the picture is different for traditional locally-installed products and for cloud-based offerings, since in the latter case it is possible to gather more complete, accurate and timely usage data.

On the “reasoning” side, the issue is why and how programmers decide to adopt a particular approach. For example, bug fixes tend to be more audacious (implying redesign if appropriate) at the beginning of a project, and more conservative as delivery nears and everyone is scared of breaking something. Another object of the study is how deeply developers understand the cause rather than just the symptom; the paper reports that 18% “did not have time to figure out why the bug occurred“. Surprising or not, I don’t know, but scary! Yet another dimension is consistency: there is a tension between providing what might ideally be the best fix and remaining consistent with the design decisions that underlie a software system throughout its architecture.

I was more impressed by the individual categories of the classification than by that classification as a whole; some of the categories appear redundant (“interface breakage“, “data propagation” and “internal vs external“, for example, seem to be pretty much the same; ditto for “cause understanding” and “accuracy“). On the other hand the paper does not explicitly claim that the categories are orthogonal. If they turn this conference presentation into a journal article I am pretty sure they will rework the classification and make it more robust. It does not matter that it is a bit shaky at the moment since the main insights are in the individual kinds of fix and fix-reasoning uncovered by the study.

The authors are from Microsoft Research (one of them was visiting faculty) and interviewed numerous programmers from various Microsoft product groups to find out how they fix bugs.

The paper is nicely written and reads easily. It includes some audacious syntax, as in “this dimension” [internal vs external] “describes how much internal code is changed versus external code is changed as part of a fix“. It has a discreet amount of humor, some of which may escape non-US readers; for example the authors explain that when approaching programmers out of the blue for the survey they tried to reassure them through the words “we are from Microsoft Research, and we are here to help“, a wry reference to the celebrated comment by Ronald Reagan (or his speechwriter) that the most dangerous words in the English language are “I am from the government, and I am here to help“. To my taste the authors include too many details about the data collection process; I would have preferred the space to be used for a more detailed discussion of the findings on bug fixes. On the other hand we all know that papers to selective conferences are written for referees, not readers, and this amount of methodological detail was probably the minimum needed to get past the reviewers (by avoiding the typical criticism, for empirical software engineering research, that the sample is too small, the questions biased etc.). Thankfully, however, there is no pedantic discussion of statistical significance; the authors openly present the results as dependent on the particular population surveyed and on the interview technique. Still, these results seem generalizable in their basic form to a large subset of the industry. I hope their publication will spawn more detailed studies.

According to the ICSE program the paper will be presented on May 23 in the Debugging session, 13:30 to 15:30.

Notes and references

[1] This article review is part of the “Reading Notes” series. General disclaimer here.

[2] European Software Engineering Conference 2013, Saint Petersburg, Russia, 18-24 August, see here.

[3] Emerson Murphy-Hill, Thomas Zimmerman, Christian Bird and Nachiappan Nagapan: The Design of Bug Fixes, in ICSE 2013, available here.

[4] AutoFix project at ETH Zurich, see project page here.

[5] Ronald Reagan speech extract on YouTube.

Software verification is progressing slowly but surely. Much of that progress is incremental: making the fundamental results applicable to real programs as they are built every day by programmers working in standard circumstances. A key condition is to minimize the amount of annotations that they have to provide.

The article mentioned in my previous post, “Program Checking With Less Hassle” [1], to be presented at VSTTE in San Francisco on Friday by its lead author, Julian Tschannen, introduces several interesting contributions in this direction. One of the surprising conclusions is that sometimes it pays to specify less. That goes against intuition: usually, the more specification information (correctness annotations) you provide the more you help the prover. But in fact partial specifications can hurt rather than help. Consider for example a swap routine with a partial specification, which actually stands in the way of a proof. If modularity is not a concern, for example if the routine is part of the code being verified rather than of a library, it may be more effective to ignore the specification and use the routine’s implementation. This is particularly appropriate for small “helper” routines such as the swap example.

This inlining technique is applicable in other cases, for example to make up for a missing precondition: assume that a helper routine will only work for x > 0 but does not state that precondition, or maybe states only the weaker one x ≥ 0 ; in the code, however, it is only called with positive arguments. If we try to verify the code modularly we will fail, as indeed we should since the routine is incorrect as a general-purpose primitive. But within the context of the code there is nothing wrong with it. Forgetting the contract of the routine if any, and instead using its actual implementation, we may be able to show that everything is fine.

Another component of the approach is to fill in preconditions that programmers have omitted because they are somehow obvious to them. For example it is tempting and common to write just a [1] > 0 rather than a /= Void and then a [1] > 0 for a detachable array a. The tool takes care of  interpreting the simpler precondition as the more complete one.

The resulting “two-step verification”, integrated into the AutoProof verification tool for Eiffel, should turn out to be an important simplification towards the goal of “Verification As a Matter Of Course” [2].

References

[1] Julian Tschannen, Carlo A. Furia, Martin Nordio and Bertrand Meyer: Program Checking With Less Hassle, in VSTTE 2013, Springer LNCS, to appear, draft available here; presentation on May 17 in the 15:30-16:30  session.

[2] Verification As a Matter Of Course, article in this blog, 29 March 2010, see here.

The following presentations from our ETH group in the ICSE week (International Conference on Software Engineering, San Francisco) address important issues of software specification and verification, describing new techniques that we have recently developed as part of our work building EVE, the Eiffel Verification Environment. One is at ICSE proper and the other at VSTTE (Verified Software: Tools, Theories, Experiments). If you are around please attend them.

Julian Tschannen will present Program Checking With Less Hassle, written with Carlo A. Furia, Martin Nordio and me, at VSTTE on May 17 in the 15:30-16:30 session (see here in the VSTTE program. The draft is available here. I will write a blog article about this work in the coming days.

Nadia Polikarpova will present What Good Are Strong Specifications?, written with , Carlo A. Furia, Yu Pei, Yi Wei and me at ICSE on May 22 in the 13:30-15:30 session (see here in the ICSE program). The draft is available here. I wrote about this paper in an earlier post: see here. It describes the systematic application of theory-based modeling to the full specification and verification of advanced software.

A core aspect of our verification work is the use of “strong” contracts, which express sophisticated specification properties without requiring a separate specification language: even for advanced properties, there is no need for a separate specification language, with special notations such as those of first-order logic; instead, one can continue to rely, in the tradition of Design by Contract, on the built-in notations of the programming language, Eiffel.

This is the idea of domain theory, as discussed in earlier posts on this blog, in particular [1]. An early description of the approach, part of Bernd Schoeller’s PhD thesis work, was [2]; the next step was [3], presented at VSTTE in 2010.

A new paper to be presented at ICSE in May [3], part of an effort led by Nadia Polikarpova for her own thesis in progress, shows new advances in using strong specifications, demonstrating their expressive power and submitting them to empirical evaluation. The results show in particular that strong specifications justify the extra effort; in particular they enable automatic tests to find significantly more bugs.

A byproduct of this work is to show again the complementarity between various forms of verification, including not only proofs but (particularly in the contribution of two of the co-authors, Yi Wei and Yu Pei, as well as Carlo Furia) tests.

References

[1] Bertrand Meyer: Domain Theory: the forgotten step in program verification, article on this blog, see here.

[2] Bernd Schoeller, Tobias Widmer and Bertrand Meyer: Making Specifications Complete Through Models, in Architecting Systems with Trustworthy Components, eds. Ralf Reussner, Judith Stafford and Clemens Szyperski, Lecture Notes in Computer Science, Springer-Verlag, 2006, available here.

[3] Nadia Polikarpova, Carlo Furia and Bertrand Meyer: Specifying Reusable Components, in Verified Software: Theories, Tools, Experiments (VSTTE ‘ 10), Edinburgh, UK, 16-19 August 2010, Lecture Notes in Computer Science, Springer Verlag, 2010, available here.

[4] Nadia Polikarpova, Carlo A. Furia, Yu Pei, Yi Wei and Bertrand Meyer: What Good Are Strong Specifications?, to appear in ICSE 2013 (Proceedings of 35th International Conference on Software Engineering), San Francisco, May 2013, draft available here.

The European Software Engineering Conference takes place every two years in connection with the ACM Foundations of Software Engineering symposium (which in even years is in the US). The next ESEC/FSE  will be held for the first time in Russia, where it will be the first major international software engineering conference ever. It comes at a time when the Russian software industry is ever more present through products and services offered worldwide. See the conference site here. The main conference will be held 21-23 August 2013, with associated events before and after so that the full dates are August 18 to 26. (I am the general chair.)

Other than ICSE, ESEC/FSE is second to none in the quality of the program. We already have four outstanding keynote speakers:  Georges Gonthier from Microsoft Research, Paola Inverardi from L’Aquila in Italy, David Notkin from U. of Washington (in whose honor a symposium will be held as an associated event of ESEC/FSE, chaired by Michael Ernst), and Moshe Vardi of Rice and of course Communications of the ACM.

Saint Petersburg is one of the most beautiful cities in the world, strewn with gilded palaces, canals, world-class museums (not just the Hermitage), and everywhere mementos of the great poets, novelists, musicians and scientists who built up its fame.

Hosted by ITMO National Research University, the conference will be held in the magnificent building of the Razumovsky Palace on the banks of the Moika river; see here.

The Call for Papers has a deadline of March 1st, so there is still plenty of time to polish your best paper and send it to ESEC/FSE. There is also still time to propose worskhops and other associated events. ESEC/FSE will be a memorable moment for the community and we hope to see many of the readers there.

In modeling object-oriented programs, for purposes of verification (proofs) or merely for a better understanding, we are faced with the unique “general relativity” property of OO programming: all the operations you write (excluding non-OO mechanisms such as static functions) are expressed relative to a “current object” which changes repeatedly during execution. More precisely at the start of a call x.r (…) and for the duration of that call the current object changes to whatever x denotes — but to determine that object we must again interpret x in the context of the previous current object. This raises a challenge for reasoning about programs; for example in a routine the notation f.some_reference, if f is a formal argument, refers to objects in the context of the calling object, and we cannot apply standard rules of substitution as in the non-OO style of handling calls.

In earlier work [1, 2] initially motivated by the development of the Alias Calculus, I introduced a notion of negative variable to deal with this issue. During the execution of a call x.r (…) the negation of x , written x’, represents a back pointer to the calling object; negative variables are characterized by axiomatic properties such as x.x’= Current and x’.(old x)= Current. Alexander Kogtenkov has implemented these ideas and refined them.

In a recent paper under submission [3], we review the concepts and applications of negative variables.

References

[1] Bertrand Meyer: Steps Towards a Theory and Calculus of Aliasing, in International Journal of Software and Informatics, 2011, available here.

[2] Bertrand Meyer: Towards a Calculus of Object Programs, in Patterns, Programming and Everything, Judith Bishop Festschrift, eds. Karin Breitman and Nigel Horspool, Springer-Verlag, 2012, pages 91-128, available here.

[3] Bertrand Meyer and Alexander Kogtenkov: Negative Variables and the Essence of Object-Oriented Programming, submitted for publication, 2012. [Updated 13 January 2014: I have removed the link to the draft mentioned in this post since it is now superseded by the new version, soon to be published, and available here.]

A couple of weeks ago I proposed a small quiz. (I also stated that the answer would come “on Wednesday” — please understand any such promise as “whenever I find the time”. Sorry.) Here is the answer.

The quiz was:

I have a function:

• For 0 it yields 0.
• For 1 it yields 1.
• For 2 it yields 4.
• For 3 it yields 9.
• For 4 it yields 16.

What is the value for 5?

Shortly thereafter I added a hint: the value for 5 is 25, and changed the question to: “What is the value for 6?”. For good measure we can also ask about the value for 1000. Now compare your answer to  what follows.

A good answer for the value at 6 is: 34 . The function in this case is -10 + 5 x + |2 x – 3| + |2 x -7|. It matches the values for the given inputs.

The value for 1000 is 8980:

Another good answer at position 6 is 35.6. It comes up if we assume the function is over reals rather than integers; then a possible formula, which correlates very well (R-square of 0.9997) with the values at the given inputs, is:

869.42645566111 (1 – 0.4325853145802 e^{-.0467615868913719  (x – 17.7342512233011)})^{2.3116827277657443}

with a quite different asymptotic behavior, giving the value 869.4 at position 1000:

Some readers might have thought of another possibility, the square function x², which again matches all the given values:

So which of these answers is right? Each is as good as the others, and as bad. There is in particular no reason to believe that the values given in the quiz’s statement suggest the square function. Any function that fits the given values, exactly (if we stick to integers) or approximately (with reals as simulated on a computer) is an equally worthy candidate. Six inputs, or six thousand, do not resolve the question. At best they are hints.

This difference between a hint and a solution is at the core of software engineering. It is, for example, the difference between a test and a specification. A test tells us that the program works for some values; as Dijkstra famously pointed out, and anyone who has developed a serious program has experienced, it does not tell us that it will work for others. The more successful tests, the more hints; but they are still only hints. I have always wondered whether Dijkstra was explicitly thinking of the Popperian notion of falsifiability: no number of experiments will prove a physical theory (although a careful experiment may boost the confidence in the theory, especially if competing theories fail to explain it, as the famous Eddington expedition did for relativity in 1919 [1]); but a single experiment can disprove a theory. Similarly, being told that our function’s value at 6 is 34 disqualifies the square function and the last one (the exponential), but does not guarantee that the first function (the linear combination) is the solution.

The specification-testing duality is the extension to computer science of the basic duality of logic. It starts with the elementary boolean operators: to prove a or b it suffices to establish a or to establish b; and to disprove a and b it suffices to show that a does not hold or to show that b does not hold. The other way round, to disprove a or b we have to show that a does not hold and to show that b does not hold; to prove that a and b holds, we have to show that a holds and to show that b holds.

Predicate calculus generalizes or to ∃, “there exists”, and and to ∀, “for all”. To prove ∃ x | p (x) (there is an x of which p holds) it suffices to find one value a such that p (a); let’s be pretentious and say we have “skolemized” x. To disprove∀ x | p (x) (p holds of all x) it suffices to find one value for which p does not hold.

In software engineering the corresponding duality is between proofs and tests, or (equivalently) specifications and use cases. A specification is like a “for all”: it tells us what must happen for all envisioned inputs. A test is like a “there exists”: it tells us what happens for a particular input and hence, as in predicate calculus, it is interesting as a disproof mechanism:

• A successful test brings little information (like learning the value for 5 when trying to figure out what a function is, or finding one true value in trying to prove a ∀ or a false value in trying to prove a ∃).
• An unsuccessful test brings us decisive information (like a false value for a ∀): the program is definitely not correct. It skolemizes incorrectness.

A proof, for its part, brings the discussion to an end when it is successful. In practice, testing may still be useful in this case, but only testing that addresses issues not covered by the proof:

• Correctness of the compiler and platform, if not themselves proved correct.
• Correctness the proof tools themselves, since most practical proofs require software support.
• Aspects not covered by the specification such as, typically, performance and usability.

But for the properties it does cover the proof is final.

It is as foolish, then, to use tests in lieu of specifications as it would be to ignore the limitations of a proof. Agile approaches have caused much confusion here; as often happens in the agile literature [2], the powerful insight is mixed up with harmful advice. The insight, which has significantly improved the practice of software development, is that the regression test suite is a key asset of a project and that tests should be run throughout. The bad advice is to ditch upfront requirements and specifications in favor of tests. The property that tests lack and specifications possess is generality. A test is an instance; a thousand tests can never be more than a thousand instances. As I pointed out in a short note in EiffelWorld (the precursor to this blog) a few years ago [3], the relationship is not symmetric: one can generate tests from a specification, but not the other way around.

The same relationship holds between use cases and requirements. It is stunning to see how many people think that use cases (scenarios) are a form of requirements. As requirements they are as useless as one or ten values are to defining a function. Use cases are a way to complement the requirements by describing the system’s behavior in selected important cases. A kind of reality check, to ensure that whatever abstract aims have been defined for the system it still covers the cases known to be of immediate interest. But to rely on use cases as requirements means that you will get a system that will satisfy the use cases — and possibly little else.

When I use systems designed in recent years, in particular Web-based systems, I often find myself in a stranglehold: I am stuck with the cases that the specifiers thought of. Maybe it’s me, but my needs tend, somehow, to fall outside of these cases. Actually it is not just me. Not long ago, I was sitting close to a small-business owner who was trying to find her way through an insurance site. Clearly the site had a planned execution path for employees, and another for administrators. Problem: she was both an employee and the administrator. I do not know how the session ended, but it was a clear case of misdesign: a system built in terms of standard scenarios. Good specification performs an extra step of abstraction (for example using object-oriented techniques and contracts, but this is for another article). Skipping this step means forsaking the principal responsibility of the requirements phase: to generalize from an analysis of the behavior in known cases to a definition of the desired behaviors in all relevant cases.

Once more, as everywhere else in computer science [4], abstraction is the key to solid results that stand the test of time. Definitely better than judging a book by its cover, inferring a function by its first few values, verifying a program by its tests, or specifying a system by its use cases.

References

[1] See e.g. a blog article: Einstein and Eddington, here.

[2] Bertrand Meyer: Agile! The Good, the Hype and the Ugly, 2013, to appear.

[3] Bertrand Meyer: Test or spec? Test and spec? Test from spec!, EiffelWorld column, 2004 available here.

[4] Jeff Kramer: Is Abstraction the Key to Computer Science?, in Communications of the ACM, vol. 50, no. 4, April 2007, pages 36-42,  available from CiteSeer here