Bertrand Meyer's technology+ blog

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.