Requirements engineering (studying and documenting what a software system should do, independently of how it will do it) took some time to be recognized as a key part of software engineering, since the early focus was, understandably, on programming. It is today a recognized sub-discipline and has benefited in the last decades from many seminal concepts. An early paper of mine, *On Formalism in Specifications* [1], came at the beginning of this evolution; it made the case for using formal (mathematics-based) approaches. One of the reasons it attracted attention is its analysis of the “seven sins of the specifier”: a list of pitfalls into which authors of specifications and requirements commonly fall.

One of the techniques presented in the paper has not made it into the standard requirements-enginering bag of tricks. I think it deserves to be known, hence the present note. There really will not be anything here that is not in the original article; in fact I will be so lazy as to reuse its example. (Current requirements research with colleagues should lead to the publication of new examples.)

Maybe the reason the idea did not register is that I did not give it a name. So here goes: *formal picnic*.

The usual software engineering curriculum includes, regrettably, no room for *field trips*. We are jealous of students and teachers of geology or zoology and their occasional excursions: once in a while you put on your boots, harness your backpack, and head out to quarries or grasslands to watch pebbles or critters *in flagrante*, after a long walk with the other boys and girls and before all having lunch together in the wild. Yes, scientific life in these disciplines really is a picnic. What I propose for the requirements process is a similar excursion; not into muddy fields, but into the dry pastures of mathematics.

The mathematical picnic process starts with a natural-language requirements document. It continues, for some part of the requirements, with a translation into a mathematical version. It terminates with a return trip into natural language.

The formal approach to requirements, based on mathematical notations (as was discussed in my paper), is still controversial; a common objection is that requirements must be understandable by ordinary project stakeholders, many of whom do not have advanced mathematical skills. I am not entering this debate here, but there can be little doubt that delicate system properties can be a useful step, if only for the requirements engineers themselves. Mathematical notation forces precision.

What, then, if we want to end up with natural language for clarity, but also to take advantage of the precision of mathematics? The formal picnic answer is that we can use mathematics as a tool to improve the requirements. The three steps are:

- Start: a natural-language requirements document. Typically too vague and deficient in other ways (the seven sins) to serve as an adequate basis for the rest of the software process, as a good requirements document should.
- Picnic: an excursion into mathematics. One of the main purposes of a requirements process is to raise and answer key questions about the system’s properties. Using mathematics helps raise the right questions and obtain precise answers. You do not need to apply the mathematical picnic to the entire system: even if the overall specification remains informal, some particularly delicate aspects may benefit from a more rigorous analysis.
- Return trip: thinking of the non-formalist stakeholders back home, we translate the mathematical descriptions into a new natural-language version.

This final version is still in (say) English, but typically not the kind of English that most people naturally write. It may in fact “sound funny”. That is because it is really just mathematical formulae translated back into English. It retains the precision and objectivity of mathematics, but is expressed in terms that anyone can understand.

Let me illustrate the mathematical picnic idea with the example from my article. For reasons that do not need to be repeated here (they are in the original), it discussed a very elementary problem of text processing: splitting a text across lines. The original statement of the problem, from a paper by Peter Naur, read:

*Given a text consisting of words separated by BLANKS or by NL (new line) characters, convert it to a line-by-line form in accordance with the following rules: (1) line breaks must be made only where the given text has BLANK or NL; (2) each line is filled as far as possible as long as (3) no line will contain more than MAXPOS characters.*

My article then cited an alternative specification proposed in a paper by testing experts John Goodenough and Susan Gerhart. G&G criticized Naur’s work (part of the still relevant debate between proponents of tests and proponents of proofs such as Naur). They pointed out deficiencies in his simple problem statement above; for example, it says nothing about the case of a text containing a word of more than MAXPOS characters. G&G stated that the issue was largely one of specification (requirements) and went on to propose a new problem description, four times as long as Naur’s. In my own article, I had a field day taking aim at their own endeavor. (Sometime later I met Susan Gerhart, who was incredibly gracious about my critique of her work, and became an esteemed colleague.) I am not going to cite the G&G replacement specification here; you can find it in my article.

Since that article’s topic was formal approaches, it provided a mathematical statement of Naur’s problem. It noted that the benefit of mathematical formalization is not just to gain precision but also to identify important questions about the problem, with a view to rooting out dangerous potential bugs. Mathematics means not just formalization but proofs. If you formalize the Naur problem, you soon realize that — as originally posed — it does not always have a solution (because of over-MAXPOS words). The process forces you to specify the conditions under which solutions do exist. This is one of the software engineering benefits of a mathematical formalization effort: if such conditions are not identified at the requirements level, they will take their revenge in the program, in the form of erroneous results and crashes.

You can find the mathematical specification (only one of several possibilities) in the article. The discussion also noted that one could start again from that spec and go back to English. That was, without the name, the mathematical picnic. The result’s length is in-between the other two versions: twice Naur’s, but half G&G’s. Here it is:

*Given are a non-negative integer MAXPOS and a character set including two “break characters” blank and newline. The program shall accept as input a finite sequence of characters and produce as output a sequence of characters satisfying the following conditions:*

* • It only differs from the input by having a single break character wherever the input has one or more break characters;*

* • Any MAXPOS + 1 consecutive characters include a newline;*

* • The number of newline characters is minimal.*

* If (and only if) an input sequence contains a group of MAXPOS + 1 consecutive nonbreak characters, there exists no such output. In this case, the program shall produce the output associated with the initial part of the sequence, up to and including the MAXPOS·th character of the first such group, and report the error.*

This post-picnic version is the result of a quasi-mechanical retranscription from the mathematical specification in the paper.

It uses the kind of English that one gets after a mathematical excursion. I wrote above that this style might sound funny; not to me in fact, because I am used to mathematical picnics, but probably to others (does it sound funny to you?).

The picnic technique provides a good combination of the precision of mathematics and the readability of English. English requirements as ordinarily written are subject to the seven sins described in my article, from ambiguity and contradiction to overspecification and noise. A formalization effort can correct these issues, but yields a mathematical text. Whether we like it or not, many people react negatively to such texts. We might wish they learn, but that is often not an option, and if they are important stakeholders we need their endorsement or correction of the requirements. With a mathematical picnic we translate the formal text back into something they will understand, while avoiding the worst problems of natural-language specifications.

Practicing the Formal Picnic method also has a long-term benefit for a software team. Having seen first-hand that better natural-language specifications (noise-free and more precise) are possible, team members little by little learn to apply the same style to the English texts they write, even without a mathematical detour.

If the goal is high-quality requirements, is there any alternative? What I have seen in many requirements documents is a fearful attempt to avoid ambiguity and imprecision by leaving no stone unturned: adding information and redundancy over and again. This was very much what I criticized in the G&G statement of requirements, which attempted to correct the deficiencies of the Naur text by throwing ever-more details that caused ever more risks of entanglement. It is fascinating to see how every explanation added in the hope of filling a possible gap creates more sources of potential confusion and a need for even more explanations. In industrial projects, this is the process that leads to thousands-of-pages documents, so formidable that they end up (as in the famous Ariane-5 case) on a shelf where no one will consult them when they would provide critical answers.

Mathematical specifications yield the precision and uncover the contradictions, but they also avoid noise and remain terse. Translating them back into English yields a reasonable tradeoff. Try a formal picnic one of these days.

### Acknowledgments

For numerous recent discussions of these and many other related topics, I am grateful to my colleagues from the Innopolis-Toulouse requirements research group: Jean-Michel Bruel, Sophie Ebersold, Florian Galinier, Manuel Mazzara and Alexander Naumchev. I remain grateful to Axel van Lamsweerde (beyond his own seminal contributions to requirements engineering) for telling me, six years after I published a version of [1] in French, that I should take the time to produce a version in English too.

### Reference

Bertrand Meyer: *On Formalism in Specifications*, in *IEEE Software*, vol. 3, no. 1, January 1985, pages 6-25. PDF available via IEEE Xplore with account, and also from here. Adapted translation of an original article in French (AFCET Software Engineering newsletter, no. 1, pages 81-122, 1979).

(*This article* was o*riginally published on the Comm. ACMM blog.*)

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