Archive for the ‘Formal methods and proofs’ Category.

Are my requirements complete?

Some important concepts of software engineering, established over the years, are not widely known in the community. One use of this blog is to provide tutorials on such overlooked ideas. An earlier article covered one pertaining to project management: the Shortest Possible Schedule property . Here is another, this time in the area of requirements engineering, also based on a publication that I consider to be a classic (it is over 40 years old) but almost unknown to practitioners.

Practitioners are indeed, as in most of my articles, the intended audience. I emphasize this point right at the start because if you glance at the rest of the text you will see that it contains (horror of horrors) some mathematical formulae, and might think “this is not for me”. It is! The mathematics is very simple and my aim is practical: to shed light on an eternal question that faces anyone writing requirements (whatever the style, traditional or agile): how can I be sure that a requirements specification is complete?

To a certain extent you cannot. But there is better answer, a remarkably simple one which, while partial, helps.

Defining completeness

The better answer is called “sufficient completeness” and comes from the theory of abstract data types. It was introduced in a 1978 article by Guttag and Horning [1]. It is also implicit in a more down-to-earth document, the 1998 IEEE standard on how to write requirements [2].

There is nothing really new in the present article; in fact my book Object-Oriented Software Construction [3] contains an extensive discussion of sufficient completeness (meant to be more broadly accessible than Guttag and Horning’s scholarly article). But few people know the concepts; in particular very few practitioners have heard of sufficient completeness (if they have heard at all of abstract data types). So I hope the present introduction will be useful.

The reason the question of determining completeness of requirements seems hopeless at first is the natural reaction: complete with respect to what? To know that the specification is complete we would need a more general description of all that our stakeholders want and all the environment constraints, but this would only push the problem further: how do we know that such description itself is complete?

That objection is correct in principle: we can never be sure that we did not forget something someone wanted, or some property that the environment imposes. But there also exist more concrete and assessable notions of completeness.

The IEEE standard gives three criteria of completeness. The first states that “all requirements” have been included, and is useless, since it  runs into the logical paradox mentioned above, and is tautological anyway (the requirements are complete if they include all requirements, thank you for the information!). The second is meaningful but of limited interest (a “bureaucratic” notion of completeness): every element in the requirements document is numbered, every cross-reference is defined and so on. The last criterion is the interesting one: “Definition of the responses of the software to all realizable classes of input data in all realizable classes of situations”. Now this is meaningful. To understand this clause we need to step back to sufficient completeness and, even before that, to abstract data types.

Abstract data types will provide our little mathematical excursion (our formal picnic in the words of an earlier article) in our study of requirements and completeness. If you are not familiar with this simple mathematical theory, which every software practitioner should know, I hope you will benefit from the introduction and example. They will enable us to introduce the notion of sufficient completeness formally before we come back to its application to requirements engineering.

Specifying an abstract data type

 Abstract data types are the mathematical basis for object-oriented programming. In fact, OO programming but also OO analysis and OO design are just a realization of this mathematical concept at various levels of abstraction, even if few OO practitioners are aware of it. (Renewed reference to [3] here if you want to know more.)

An ADT (abstract data type) is a set of objects characterized not by their internal properties (what they are) but by the operations applicable to them (what they have), and the properties of these operations. If you are familiar with OO programming you will recognize that this is exactly, at the implementation level, what a class is. But here we are talking about mathematical objects and we do not need to consider implementation.

An example  of a type defined in this way, as an ADT, is a notion of POINT on a line. We do not say how this object is represented (a concept that is irrelevant at the specification level) but how it appears to the rest of the world: we can create a new point at the origin, ask for the coordinate of a point, or move the point by a certain displacement. The example is the simplest meaningful one possible, but it gives the ideas.

adt

An ADT specification has three part: Functions, Preconditions and Axioms. Let us see them (skipping Preconditions for the moment) for the definition of the POINT abstract data type.

The functions are the operations that characterize the type. There are three kinds of function, defined by where the ADT under definition, here POINT, appears:

  • Creators, where the type appears only among the results.
  • Queries, where it appears only among the arguments.
  • Commands, where it appears on both sides.

There is only one creator here:

new: → POINT

new is a function that takes no argument, and yields a point (the origin). We will write the result as just new (rather than using empty parentheses as in new ()).

Creators correspond in OO programming to constructors of a class (creation procedures in Eiffel). Like constructors, creators may have arguments: for example instead of always creating a point at the origin we could decide that new creates a point with a given coordinate, specifying it as INTEGER → POINT and using it as new (i) for some integer i (our points will have integer coordinates). Here for simplicity we choose a creator without arguments. In any case the new type, here POINT, appears only on the side of the results.

Every useful ADT specification needs at least one creator, without which we would never obtain any objects of the type (here any points) to work with.

There is also only one query:

x: POINT → INTEGER

 which gives us the position of a point, written x (p) for a point p. More generally, a query enables us to obtain properties of objects of the new type. These properties must be expressed in terms of types that we have already defined, like INTEGER here. Again there has to be at least one query, otherwise we could never obtain usable information (information expressed in terms of what we already know) about objects of the new type. In OO programming, queries correspond to fields (attributes) of a class and functions without side effects.

And we also have just one command:

move: POINT × INTEGER → POINT

a function that for any point p and integer i and yields a new point, move (p, i).  Again an ADT specification is not interesting unless it has at least one command, representing ways to modify objects. (In mathematics we do not actually modify objects, we get new objects. In imperative programming we will actually update existing objects.) In the classes of object-oriented programming, commands correspond to procedures (methods which may change objects).

You see the idea: define the notion of POINT through the applicable operations.

Listing their names and the types of their arguments types results (as in POINT × INTEGER → POINT) is not quite enough to specify these operations: we must specify their fundamental properties, without of course resorting to a programming implementation. That is the role of the second component of an ADT specification, the axioms.

For example I wrote above that new yields the origin, the point for which x = 0,  but you only had my word for it. My word is good but not good enough. An axiom will give you this property unambiguously:

x (new) = 0                                    — A0

The second axiom, which is also the last, tells us what move actually does. It applies to any point p and any integer m:

x (move (p, m)) = x (p) + m       — A1

In words: the coordinate of the point resulting from moving p by m is the coordinate of p plus m.

That’s it! (Except for the notion of precondition, which will wait a bit.) The example is trivial but this approach can be applied to any number of  data types, with any number of applicable operations and any level of complexity. That is what we do, at the design and implementation level, when writing classes in OO programming.

Is my ADT sufficiently complete?

Sufficient completeness is a property that we can assess on such specifications. An ADT specification for a type T (here POINT) is sufficiently complete if the axioms are powerful enough to yield the value of any well-formed query expression in a form not involving T. This definition contains a few new terms but the concepts are very simple; I will explain what it means through an example.

With an ADT specification we can form all kinds of expressions, representing arbitrarily complex specifications. For example:

x (move (move (move (new, 3), x (move (move (new, -2), 4))), -6))

This expression will yield an integer (since function x has INTEGER as its result type) describing the result of a computation with points. We can visualize this computation graphically; note that it involves creating two points (since there are two occurrences of new) and moving them, using in one case the current coordinate of one of them as displacement for the other. The following figure illustrates the process.

computation

The result, obtained informally by drawing this picture, is the x of P5, that is to say -1. We will derive it mathematically below.

Alternatively, if like most programmers (and many other people) you find it more intuitive to reason operationally than mathematically, you may think of the previous expression as describing the result of the following OO program (with variables of type POINT):

create p                                — In C++/Java syntax: p = new POINT();
create q
p.move (3)
q.move (-2)
q.move (4)
p.move (q.x)
p.move (-6)

Result := p.x

You can run this program in your favorite OO programming language, using a class POINT with new, x and move, and print the value of Result, which will be -1.

Here, however, we will stay at the mathematical level and simplify the expression using the axioms of the ADT, the same way we would compute any other mathematical formula, applying the rules without needing to rely on intuition or operational reasoning. Here is the expression again (let’s call it i, of type INTEGER):

ix (move (move (move (new, 3), x (move (move (new, -2), 4))), -6))

A query expression is one in which the outermost function being applied, here x, is a query function. Remember that a query function is one which the new type, here POINT, appears only on the left. This is the case with x, so the above expression i is indeed a query expression.

For sufficient completeness, query expressions are the ones of interest because their value is expressed in terms of things we already know, like INTEGERs, so they are the only way we can concretely obtain directly usable information the ADT (to de-abstract it, so to speak).

But we can only get such a value by applying the axioms. So the axioms are “sufficiently complete” if they always give us the answer: the value of any such query expression.

 Let us see if the above expression i satisfies this condition of sufficient completeness. To make it more tractable let us write  it in terms of simpler expressions (all of type POINT), as illustrated by the figure below:

p1 = move (new, 3)
p2= move (new, -2)
p3= move (p2, 4)
p4= move (p1, x (p3))
p5= move (p4, -6)
i = x (p5)

expression

(You may note that the intermediate expressions roughly correspond to the steps in the above interpretation of the computation as a program. They also appear in the illustrative figure repeated below.)

computation

Now we start applying the axioms to evaluating the expressions. Remember that we have two axioms: A0 tells us that x (new) = 0 and A1 that x (move (p, m)) = x (p) + m. Applying A1 to the definition the expression i yields

i = x (p4) – 6
= i4 – 6

if we define

i4 = x (p4)      — Of type INTEGER

We just have to compute i4. Applying A1 to the definion of p4 tells us that

i4 = x (p1) + x (p3)

To compute the two terms:

  • Applying A1 again, we see that the first term x (p1) is x (new) + 3, but then A0 tells us that x (new) is zero, so x (p1) is 3.
  • As to x (p3), it is, once more from A1, x (p2) + 4, and x (p2) is (from A1 then A0), just -2, so x (p3) is 2.

In the end, then, i4 is 5, and the value of the entire expression i = i4 – 6 is -1. Good job!

Proving sufficient completeness

The successful computation of i was just a derivation for one example, showing that in that particular case the axioms yield the answer in terms of an INTEGER. How do we go from one example to an entire specification?

The bad news first: like all interesting problems in programming, sufficient completeness of an ADT specification is theoretically undecidable. There is no general automatic procedure that will process an ADT specification and print out ““sufficiently complete” or “not sufficiently complete”.

Now that you have recovered from the shock, you can share the computer scientist’s natural reaction to such an announcement: so what. (In fact we might define the very notion of computer scientist as someone who, even before he brushes his teeth in the morning — if he brushes them at all — has already built the outline of a practical solution to an undecidable problem.) It is enough that we can find a way to determine if a given specification is sufficiently complete. Such a proof is, in fact, the computer scientist’s version of dental hygiene: no ADT is ready for prime time unless it is sufficiently complete.

The proof is usually not too hard and will follow the general style illustrated for our simple example.

We note that the definition of sufficient completeness said: “the axioms are powerful enough to yield the value of any well-formed query expression in a form not involving the type”. I have not defined “well-formed” yet. It simply means that the expressions are properly structured, with the proper syntax (basically the correct matching of parentheses) and proper number and types of arguments. For example the following are not well-formed (if p is an expression of type POINT):

move (p, 55(     — Bad use of parentheses.
move (p)            — Wrong number of arguments.
move (p, p)       — Wrong type: second argument should be an integer.

Such expressions are nonsense, so we only care about well-formed expressions. Note that in addition to new, x and move , an expression can use integer constants as in the example (although we could generalize to arbitrary integer expressions). We consider an integer constant as a query expression.

We have to prove that with the two axioms A0 and A1 we can determine the value of any query expression i. Note that since the only query functions is x, the only possible form for i, other than an integer constant, is x (p) for some expression p of type POINT.

The proof proceeds by induction on the number n of parenthesis pairs in a query expression i.

There are two base steps:

  • n = 0: in that case i can only be an integer constant. (The only expression with no parentheses built out of the ADT’s functions is new, and it is not a query expression.) So the value is known. In all other cases i will be of the form x (p) as noted.
  • n = 1: in that case p  can only be new, in other words i = x (new), since the only function that yields points, other than new, is move, and any use of it would add parentheses. In this case axiom A0 gives us the value of i: zero.

For the induction step, we consider i with n + 1 parenthesis pairs for n > 1. As noted, i is of the form x (p), so p has exactly n parenthesis pairs. p cannot be new (which would give 0 parenthesis pairs and was taken care of in the second base step), so p has to be of the form

p =  move (p’, i’)    — For expressions p’ of type POINT and i’ of type INTEGER.

implying (since i = x (p)) that by axiom A1, the value of i is

x (p’) + i’

So we will be able to determine the value of i if we can determine the value of both x (p’) and i’. Since p has n parenthesis pairs and p =  move (p’, i’), both p’ and i’ have at most n – 1 parenthesis pairs. (This use of n – 1 is legitimate because we have two base steps, enabling us to assume n > 1.) As a consequence, both x (p’) and i’ have at most n parenthesis pairs, enabling us to deduce their values, and hence the value of i, by the induction hypothesis.

Most proofs of sufficient completeness in my experience follow this style: induction on the number of parenthesis pairs (or the maximum nesting level).

Preconditions

I left until now the third component of a general ADT specification: preconditions. The need for preconditions arises because most practical specifications need some of their functions to be partial. A partial function from X to Y is a function that may not yield a value for some elements of X. For example, the inverse function on real numbers, which yields 1 / a for x, is partial  since it is not defined for a = 0 (or, on a computer, for non-zero but very small a).

Assume that in our examples we only want to accept points that lie in the interval [-4, +4]:

limited

 We can simply model this property by turning move into a partial function. It was specified above as

move: POINT × INTEGER → POINT

The ordinary arrow → introduces a total (always defined) function. For a partial function we will use a crossed arrow ⇸, specifying the function as

move: POINT × INTEGER ⇸ POINT

Other functions remain unchanged. Partial functions cause trouble: for f in X ⇸ Y we can no longer cheerfully use f (x) if f is a partial function, even for x of the appropriate type X. We have to make sure that x belongs to the domain of f, meaning the set of values for which f is defined. There is no way around it: if you want your specification to be meaningful and it uses partial functions, you must specify explicitly the domain of each of them. Here is how to do it, in the case of move:

move (p: POINT; d: INTEGER) require |x (p) + d | < 5    — where |…| is absolute value

To adapt the definition (and proofs) of sufficient completeness to the possible presence of partial functions:

  • We only need to consider (for the rule that axioms must yield the value of query expressions) well-formed expressions that satisfy the associated preconditions.
  • The definition must, however, include the property that axioms always enable us to determine whether an expression satisfies the associated preconditions (normally a straightforward part of the proof since preconditions are themselves query expressions).

Updating the preceding proof accordingly is not hard.

Back to requirements

The definition of sufficient completeness is of great help to assess the completeness of a requirements document. We must first regretfully note that for many teams today requirements stop at  “use cases” (scenarios) or  “user stories”. Of course these are not requirements; they only describe individual cases and are to requirements what tests are to programs. They can serve to check requirements, but do not suffice as requirements. I am assuming real requirements, which include descriptions of behavior (along with other elements such as environment properties and project properties). To describe behaviors, you will define operations and their effects. Now we know what the old IEEE standard is telling us by stating that complete requirements should include

definition of the responses of the software to all realizable classes of input data in all realizable classes of situations

Whether or not we have taken the trouble to specify the ADTs, they are there in the background; our system’s operations reflect the commands, and the effects we can observe reflect the queries. To make our specification complete, we should draw as much as possible of the (mental or explicit) matrix of possible effects of all commands on all queries. “As much as possible” because software engineering is engineering and we will seldom be able to reach perfection. But the degree of fullness of the matrix tells us a lot (possible software metric here?) about how close our requirements are to completeness.

I should note that there are other aspects to completeness of requirements. For example the work of Michael Jackson, Pamela Zave and Axel van Lamsweerde (more in some later article, with full references) distinguishes between business goals, environment constraints and system properties, leading to a notion of completeness as how much the system properties meet the goals and obey the constraints [4]. Sufficient completeness operates at the system level and, together with its theoretical basis, is one of those seminal concepts that every practicing software engineer or project manager should master.

References and notes

[1] John V. Guttag, Jim J. Horning: The Algebraic Specification of Abstract Data Types, in Acta Informatica, vol. 10, no. 1, pages 27-52, 1978, available here from the Springer site. This is a classic paper but I note that few people know it today; in Google Scholar I see over 700 citations but less than 100 of them in the past 8 years.

[2]  IEEE: Recommended Practice for Software Requirements Specifications, IEEE Standard 830-1998, 1998. This standard is supposed to be obsolete and replaced by newer ones, more detailed and verbose, but it remains the better reference: plain, modest and widely applied by the industry. It does need an update, but a good one.

[3] Bertrand Meyer, Object-Oriented Software Construction, 2nd edition, Prentice Hall, 1997. The discussion of sufficient completeness was in fact already there in the first edition from 1988.

[4] With thanks to Elisabetta Di Nitto from Politecnico di Milano for bringing up this notion of requirements completeness.

Recycled A version of this article was first published on the Communications of the ACM blog.

 

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Formality in requirements: new publication

The best way to make software requirements precise is to use one of the available “formal” approaches. Many have been proposed; I am not aware of a general survey published so far. Over the past two years, we have been working on a comprehensive survey of the use of formality in requirements, of which we are now releasing a draft. “We” is a joint informal research group from Innopolis University and the University of Toulouse, whose members have been cooperating on requirements issues, resulting in publications listed  under “References” below and in several scientific events.

The survey is still being revised, in particular because it is longer than the page limit of its intended venue (ACM Computing Surveys), and some sections are in need of improvement. We think, however, that the current draft can already provide a solid reference in this fundamental area of software engineering.

The paper covers a broad selection of methods, altogether 22 of them, all the way from completely informal to strictly formal. They are grouped into five categories: natural language, semi-formal, automata- or graph-based, other mathematical frameworks, programming-language based. Examples include SysML, Relax, Statecharts, VDM, Eiffel (as a requirements notation), Event-B, Alloy. For every method, the text proposes a version of a running example (the Landing Gear System, already used in some of our previous publications) expressed in the corresponding notation. It evaluates the methods using a set of carefully defined criteria.

The paper is: Jean-Michel Bruel, Sophie Ébersold, Florian Galinier, Alexandr Naumchev, Manuel Mazzara and Bertrand Meyer: Formality in Software Requirements, draft, November 2019.

The text is available here. Comments on the draft are welcome.

References

Bertrand Meyer, Jean-Michel Bruel, Sophie Ebersold, Florian Galinier and Alexandr Naumchev: Towards an Anatomy of Software Requirements, in TOOLS 2019, pages 10-40, see here (or arXiv version here). I will write a separate blog article about this publication.

Alexandr Naumchev and Bertrand Meyer: Seamless requirements. Computer Languages, Systems & Structures 49, 2017, pages 119-132, available here.

Florian Galinier, Jean-Michel Bruel, Sophie Ebersold and Bertrand Meyer: Seamless Integration of Multirequirements, in Complex Systems, 25th International Requirements Engineering Conference Workshop, IEEE, pages 21-25, 2017, available here.

Alexandr Naumchev, Manuel Mazzara, Bertrand Meyer, Jean-Michel Bruel, Florian Galinier and Sophie Ebersold: A contract-based method to specify stimulus-response requirements, Proceedings of the Institute for System Programming, vol. 29, issue 4, 2017, pp. 39-54. DOI: 10.15514, available here.

Alexandr Naumchev and Bertrand Meyer: Complete Contracts through Specification Drivers., in 10th International Symposium on Theoretical Aspects of Software Engineering (TASE), pages 160-167, 2016, available here.

Alexandr Naumchev, Bertrand Meyer and Víctor Rivera: Unifying Requirements and Code: An Example, in PSI 2015 (Ershov conference, Perspective of System Informatics), pages 233-244, available here.

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Sunrise was foggy today

Once you have learned the benefits of formally expressing requirements, you keep noticing potential ambiguities and other deficiencies [1] in everyday language. Most such cases are only worth a passing smile, but here’s one that perhaps can serve to illustrate a point with business analysts in your next requirements engineering workshop or with students in your next software engineering lecture.

As a customer of the Swiss telecommunications company Sunrise I receive an occasional “news” email. (As a customer of the Swiss telecommunications company Sunrise I would actually prefer that they spend my money improving  bandwidth,  but let us not digress.) Rather than raw marketing messages these are tips for everyday life, with the presumed intent of ingratiating the populace. For example, today’s message helpfully advises me on how to move house. The admirable advice starts (my translation):

10.7% of all Swiss people relocate every year. Is that your case too for next Autumn?

Actually no, it’s not my case (neither a case of being one of the “Swiss people” nor a case of intending to relocate this Fall). And, ah, the beauty of ridiculously precise statistics! Not 10.8% or 10.6%, mind you, no, 10.7% exactly! But consider the first sentence and think of something similar appearing in a requirements document or user story. Something similar does appear in such documents, all the time, leading to confusions for the programmers interpreting them and to bugs in the resulting systems. Those restless Swiss! Did you know that they include an itchy group, exactly 922,046 people (I will not be out-significant-digited!), who relocate every year?

Do not be silly, I hear you saying. What Sunrise is sharing of its wisdom is that every year a tenth of the Swiss population moves, but not the same tenth every year. Well, OK, maybe I am being silly. But if you think of a programmer reading such a statement about some unfamiliar domain (not one about which we can rely on common sense), the risk of confusion and consequent bugs is serious.

As [1] illustrated in detail, staying within the boundaries of natural language to resolve such possible ambiguities only results in convoluted requirements that make matters worse. The only practical way out is, for delicate system properties, to use precise language, also known technically as “mathematics”.

Here for example a precise formulation of the two possible interpretations removes any doubt. Let Swiss denote the set of Swiss people and  E the number of elements (cardinal) of a finite set E, which we can apply to the example because the set of Swiss people is indeed finite. Let us define slice as the Sunrise-official number of Swiss people relocating yearly, i.e. slice = Swiss ∗ 0.107 (the actual value appeared above). Then one interpretation of the fascinating Sunrise-official fact is:

{s: Swiss | (∀y: Year | s.is_moving (y))} = slice

In words: the cardinal of the set of Swiss people who move every year (i.e., such that for every year y they move during y) is equal to the size of the asserted population subset.

The other possible interpretation, the one we suspect would be officially preferred by the Sunrise powers (any formal-methods fan from Sunrise marketing reading this, please confirm or deny!), is:

∀y: Year | {s: Swiss | s.is_moving (y)} = slice

In words: for any year y, the cardinal of the set of Swiss people who move during y is equal to the size of the asserted subset.

This example is typical of where and why we need mathematics in software requirements. No absolutist stance here, no decree  that everything become formal (mathematical). Natural language is not going into retirement any time soon. But whenever one spots a possible ambiguity or imprecision, the immediate reaction should always be to express the concepts mathematically.

To anyone who has had a successful exposure to formal methods this reaction is automatic. But I keep getting astounded not only by  the total lack of awareness of these simple ideas among the overwhelming majority of software professionals, but also by their absence from the standard curriculum of even top universities. Most students graduate in computer science without ever having heard such a discussion. Where a formal methods course does exist, it is generally as a specialized topic reserved for a small minority, disconnected (as Leslie Lamport has observed [2]) from the standard teaching of programming and software engineering.

In fact all software engineers should possess the ability to go formal when and where needed. That skill is not hard to learn and should be practiced as part of the standard curriculum. Otherwise we keep training the equivalent of electricians rather than electrical engineers, programmers keep making damaging mistakes from misunderstanding ambiguous or inconsistent requirements, and we all keep suffering from buggy programs.

 

References

[1] Self-citation appropriate here: Bertrand Meyer: On Formalism in Specifications, IEEE Software, vol. 3, no. 1, January 1985, pages 6-25, available here.

[2] Leslie Lamport: The Future of Computing: Logic or Biology, text of a talk given at Christian Albrechts University, Kiel on 11 July 2003, available here.

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Soundness and completeness: with precision

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

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Blue hair and tenure track

Interview (in Russian) of Nadia Polikarpova (who proved the correctness of the EiffelBase 2 library in her PhD at ETH and is now an assistant professor at UCSD) on the site of her original university, ITMO. She explains the US tenure-track system to Europeans — good luck! She also says that programming language people are nicer than systems people; really?

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Festina retro

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 download speed

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.

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AutoProof workshop: Verification As a Matter of Course

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.

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Design by Contract: ACM Webinar this Thursday

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.

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New paper: Theory of Programs

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.

 

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Framing the frame problem (new paper)

Among the open problems of verification, particularly the verification of object-oriented programs, one of the most vexing is framing: how to specify and verify what programs element do not change. Continuing previous work, this article presents a “double frame inference” method, automatic on both sides the specification and verification sides. There is no need to write frame specifications: they will be inferred from routine postconditions. For verification, the method computes the set of actually changed properties through a “change calculus”, itself based on the previously developed alias calculus.

Some verification techniques, such as Hoare-style proofs, require significant annotation effort and potentially yield full functional verification; others, such as model checking and abstract interpretation, have more limited goals but seek full automation. Framing, in my opinion, should be automatic, freeing the programmer-verifier to devote the annotation effort to truly interesting properties.

Reference

[1] Bertrand Meyer: Framing the Frame Problem, in Dependable Software Systems, Proceedings of August 2014 Marktoberdorf summer school, eds. Alexander Pretschner, Manfred Broy and Maximilian Irlbeck, NATO Science for Peace and Security, Series D: Information and Communication Security, Springer, 2015 (to appear), pages 174-185; preprint available here.

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Detecting deadlock automatically? (New paper)

To verify sequential programs, we have to prove that they do the right thing, but also that they do it within our lifetime — that they terminate. The termination problem is considerably harder with concurrent programs, since they add a new form of non-termination: deadlock. A set of concurrent processes or threads will deadlock if they end up each holding a resource that another wants and wanting a resource that another holds.

There is no general solution to the deadlock problem, even a good enough general solution. (“Good enough” is the best we can hope for, since like many important problems deadlock is undecidable.) It is already hard enough to provide run-time deadlock detection, to be able at least to cancel execution when deadlock happens. The research reported in this new paper [1] pursues the harder goal of static detection. It applies to an object-oriented context (specifically the SCOOP model of concurrent OO computation) and relies fundamentally on the alias calculus, a static alias analysis technique developed in previous publications.

The approach is at its inception and considerable work remains to be done. Still, the example handled by the paper is encouraging: analyzing two versions of the dining philosophers problem and proving — manually — that one can deadlock and the other cannot.

References

[1] Bertrand Meyer: An automatic technique for static deadlock prevention, in PSI 2014 (Ershov Informatics Conference), eds. Irina Virbitskaite and Andrei Voronkov, Lecture Notes in Computer Science, Springer, 2015, to appear.; draft available here.

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Non-morganatic specifications

I have temporarily withdrawn this article because the specific case it used as an example has changed. I will re-publish it as soon as the situation has stabilized.

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Attached by default?

 

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).

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Code matters

(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.

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New article: contracts in practice

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.

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Eiffel as an expression language

A functional-programming style, or more generally a style involving more expressions and fewer instructions, is possible in Eiffel. In particular, Eiffel’s agent mechanism embeds a full functional-programming mechanism in the object-oriented framework of the language.

To make the notations simpler, we are discussing and tentatively implementing a number of proposed extensions. They involve no fundamental new language mechanisms, but provide new, more concise notations for existing mechanisms. Examples are:

  • Conditional expressions.
  • Implicit tuple, a rule allowing the omission of brackets for an actual argument when it is a tuple and the last argument, e.g. f (x, y, z) as an abbreviation for f ([x, y, z]) (an example involving just one argument). Tuples already provided the equivalent of a variable-argument (“varargs”) facility, but it is made simpler to use with this convention.
  • Parenthesis alias, making it possible to write just f (x, y) when f is an agent (closure, lambda expression, delegate etc. in other terminologies), i.e. treating f as if it were a function; the notation is simply an abbreviation for f.item ([x, y]) (an example that also takes advantage of implicit tuples). It has many other applications since a “parenthesis alias” can be defined for a feature of any class.
  • Avoiding explicit assignments to Result.
  • Type inference (to avoid explicitly specifying the type when it can be deduced from the context). This is a facility for the programmer, useful in particular for local variables, but does not affect the type system: Eiffel remains strongly typed, it is just that you can be lazy about writing the type when there is no ambiguity.
  • In the same vein, omitting the entire list of generic parameters when it can be inferred.

The description of the mechanism (see the link in [1]) is in the form of a set of slides explaining the concepts and presenting example. This is a working document and feedback is welcome.

References

[1] Eiffel as an expression language, Eiffel Software working document, 2012-2014, see here.

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LASER 2014 (Elba, September)

2014 marks the 10-th anniversary (11th edition) of the LASER summer school. The school will be held September 7-14, 2014, and the detailed information is here.

LASER (the name means Laboratory for Applied Software Engineering Research) is dedicated to practical software engineering. The roster of speakers since we started is a who’s who of innovators in the field. Some of the flavor of the school can gathered from the three proceedings volumes published in Springer LNCS (more on the way) or simply by browsing the pages of the schools from previous years.

Usually we have a theme, but to mark this anniversary we decided to go for speakers first; we do have a title, “Leading-Edge Software Engineering”, but broad enough to encompass a wide variety of a broad range of topics presented by star speakers: Harald Gall, Daniel Jackson, Michael Jackson, Erik Meijer (appearing at LASER for the third time!), Gail Murphy and Moshe Vardi. With such a cast you can expect to learn something important regardless of your own primary specialty.

LASER is unique in its setting: a 5-star hotel in the island paradise of Elba, with outstanding food and countless opportunities for exploring the marvelous land, the beaches, the sea, the geology (since antiquity Elba has been famous for its stones and minerals) and the history, from the Romans to Napoleon, who in the 9 months of his reign changed the island forever. The school is serious stuff (8:30 to 13 and 17 to 20 every day), but with enough time to enjoy the surroundings.

Registration is open now.

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Negative variables: new version

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.

Negative variable as back pointer

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.

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Saint Petersburg Software Engineering Seminar: 14 January 2014 (6 PM)

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.

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New paper: alias calculus and frame inference

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.

 

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Smaller, better textbook

A new version of my Touch of Class [1] programming textbook is available. It is not quite a new edition but more than just a new printing. All the typos that had been reported as of a few months ago have been corrected.

The format is also significantly smaller. This change is more than a trifle. When а  reader told me for the first time “really nice book, pity it is so heavy!”, I commiserated and did not pay much attention. After twenty people said that, and many more after them, including professors looking for textbooks for their introductory programming classes, I realized it was a big deal. The reason the book was big and heavy was not so much the size of the contents (876 is not small, but not outrageous for a textbook introducing all the fundamental concepts of programming). Rather, it is a technical matter: the text is printed in color, and Springer really wanted to do a good job, choosing thick enough paper that the colors would not seep though. In addition I chose a big font to make the text readable, resulting in a large format. In fact I overdid it; the font is bigger than necessary, even for readers who do not all have the good near-reading sight of a typical 19-year-old student.

We kept the color and the good paper,  but reduced the font size and hence the length and width. The result is still very readable, and much more portable. I am happy to make my contribution to reducing energy consumption (at ETH alone, think of the burden on Switzerland’s global energy bid of 200+ students carrying the book — as I hope they do — every morning on the buses, trains and trams crisscrossing the city!).

Springer also provides electronic access.

Touch of Class is the textbook developed on the basis of the Introduction to Programming course [2], which I have taught at ETH Zurich for the last ten years. It provides a broad overview of programming, starting at an elementary level (zeros and ones!) and encompassing topics not usually covered in introductory courses, even a short introduction to lambda calculus. You can get an idea of the style of coverage of such topics by looking up the sample chapter on recursion at touch.ethz.ch. Examples of other topics covered include a general introduction to software engineering and software tools. The presentation uses full-fledged object-oriented concepts (including inheritance, polymorphism, genericity) right from the start, and Design by Contract throughout. Based on the “inverted curriculum” ideas on which I published a number of articles, it presents students with a library of reusable components, the Traffic library for graphical modeling of traffic in a city, and builds on this infrastructure both to teach students abstraction (reusing code through interfaces including contracts) and to provide them models of high-quality code for imitation and inspiration.

For more details see the article on this blog that introduced the book when it was first published [3].

References

[1] Bertrand Meyer, Touch of Class: An Introduction to Programming Well Using Objects and Contracts, Springer Verlag, 2nd printing, 2013. The Amazon page is here. See the book’s own page (with slides and other teaching materials, sample chapter etc.) here. (Also available in Russian, see here.)

[2] Einführung in die Programmierung (Introduction to Programming) course, English course page here.

[3] Touch of Class published, article on this blog, 11 August 2009, see [1] here.

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The invariants of key algorithms (new paper)

 

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.

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Specify less to prove more

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 smallhelper 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.

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Presentations at ICSE and VSTTE

 

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.

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Multirequirements (new paper)

 

As part of a Festschrift volume for Martin Glinz of the university of Zurich I wrote a paper [1] describing a general approach to requirements that I have been practicing and developing for a while, and presented in a couple of talks. The basic idea is to rely on object-oriented techniques, including contracts for the semantics, and to weave several levels of discourse: natural-language, formal and graphical.

Reference

[1] Bertrand Meyer: Multirequirements, to appear in Martin Glinz Festschrift, eds. Anne Koziolek and Norbert Scheyff, 2013, available here.

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Negative variables and the essence of object-oriented programming (new paper)

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.

Negative variable as back pointer

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.]

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A fundamental duality of software engineering

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.

Linear, small values

 

 

 

 

 

 

 

 

 

The value for 1000 is 8980:

Linear function, full range

 

 

 

 

 

 

 

 

 

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

Exponential function, initial range

 

 

 

 

 

 

 

 

 

 

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

Exponential, full range

 

 

 

 

 

 

 

 

 

 

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

Square function, initial range

 

 

 

 

 

 

 

 

 

 

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

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Precedent

Alexander Kogtenkov pointed out to me that precursor work to my papers on the Alias Calculus [1] [2] had been published by John Whaley and Martin Rinard [3]. There are some significant differences; in particular my rules are simpler, and their work is not explicitly presented as a calculus. But many of the basic ideas are the same. The reason I did not cite that paper is simply that I was not aware of it; I am happy to correct the omission.

References

[1] Bertrand Meyer: Towards a Theory and Calculus of Aliasing, in Journal of Object Technology, vol. 9, no. 2, March-April 2010, pages 37-74, available here (superseded by [2])
[2] Bertrand Meyer: Steps Towards a Theory and Calculus of Aliasing, in International Journal of Software and Informatics, 2011, available here (revised and improved version of [1].)
[3] John Whaley and Martin Rinard: Compositional Pointer and Escape Analysis for Java Programs, in POPL 1999, available here.

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Domain Theory: precedents

Both Gary Leavens and Jim Horning commented (partly here, partly on Facebook) about my Domain Theory article [1] to mention that Larch had mechanisms for domain modeling and specification reuse. As Horning writes:

The Larch Shared Language was really all about creating reusable domain theories, including theorems about the domains.  See, for example [2] and [3].

I am honored that they found the time to write about the article and happy to acknowledge Larch, one of the most extensive efforts, over several decades, to provide serious notations and tools for specification. Leavens’s and Horning’s messages gave me the opportunity to re-read some Larch papers and discover a couple I did not know.

My article did not try to provide exhaustive references; if it had, Larch would have been among them. I would probably have cited my own paper on M [4], earlier than [3], which introduces a notation for composing specifications; see section 1.4 (“Features of the M method and the associated notation have thus been devised to allow for modular descriptions of systems. A system description may include an interface paragraph that describes the connection of the current specification with others, existing or yet to be written”) and the  presentation of these mechanisms in section 5.

Larch traits, described in [3], pursue a similar aim, but the earlier article cited by Horning [2] is a general, informal discussion of formal specification; it does not mention traits, and in fact does not cite Larch, stating instead “We have experimented with the use of two very different tools, PIE and Affirm, in constructing modest sized algebraic specifications”. Its general observations about the specification task remain useful today, and it does mention reuse in passing.

If we were to look for precedents, the basic source would have to be the Clear specification language of Goguen and Burstall, for which the citations [5, 6, 7] all appear in my M paper [4] and go back further: 1977-1981. Clear made a convincing case for modularizing specifications, and defined supporting language constructs.

Since these early publications, many people have come to realize that reuse and composition can be as useful on the specification side as they are for programming. Typical specification and verification techniques, however, do not take advantage of this idea and tend to make us restart every time from the lowest level. Domain Theory, as outlined in [1], is intended to bring abstraction, which has proved so beneficial in other parts of software engineering, to the world of specification.

References

[1] Domain Theory: The Forgotten step in program verification, an article in this blog, see here.

[2] John V. Guttag, James J. Horning, Jeannette M. Wing: Some Notes on Putting Formal Specifications to Productive Use, in Science of Computer Programming, vol. 2, no. 1, 1982, pages 53-68. (BM note: I found a copy here.)

[3] John V. Guttag, James J. Horning: A Larch Shared Language Handbook, in Science of Computer Programming, vol. 6, no. 2, 1986, pages 135-157. (BM note: I found a copy here, which also has a link to the Larch report.)

[4] Bertrand Meyer: M: A System Description Method, Technical Report TR CS 85-15, University of California, Santa Barbara, 1985, available here.

[5] Rod M. Burstall and Joe A. Goguen: Putting Theories Together to Make Specifications, in Proceedings of 5th International Joint Conference on Artificial Intelligence, Cambridge (Mass.), 1977, pages 1045- 1058.

[6] Rod M. Burstall and Joe A. Goguen: “The Semantics of Clear, a Specification Language,” in Proceedings of Advanced Course on Abstract Software Specifications, Copenhagen, Lecture Notes on Computer Science 86, Copenhagen, Springer-Verlag, 1980, pages 292-332, available here.

[7] Rod M. Burstall and Joe A. Goguen: An Informal Introduction to Specifications using Clear, in The Correctness Problem in Computer Science, eds R. S. Boyer and JJ. S. Moore, Springer-Verlag, 1981, pages 185-213.

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Aliasing and framing: Saint Petersburg seminar next week

In  last Thursday’s session of the seminar, Kokichi Futatsugi’s talk took longer than planned (and it would have been a pity to stop him), so I postponed my own talk on Automatic inference of frame conditions through the alias calculus to next week (Thursday local date). As usual it will be broadcast live.

Seminar page: here, including the link to follow the webcast.

Time and date: 5 April 2012, 18 Saint Petersburg time; you can see the local time at your location here.

Abstract:

Frame specifications, the description of what does not change in a routine call, are one of the most annoying components of verification, in particular for object-oriented software. Ideally frame conditions should be inferred automatically. I will present how the alias calculus, described in recent papers, can address this need.

There may be a second talk, on hybrid systems, by Sergey Velder.

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