Bertrand Meyer's technology+ blog

July 14 (still here for 15 minutes) is not a bad opportunity to announced the publication of a new book: The French School of Programming.

The book is a collection of chapters, thirteen of them, by rock stars of programming and software engineering research (plus me), preceded by a Foreword by Jim Woodcock and a Preface by me. The chapters are all by a single author, reflecting the importance that the authors attached to the project. Split into four sections after chapter 1, the chapters are, in order:

1. The French School of Programming: A Personal View, by Gérard Berry (serving as a general presentation of the subsequent chapters).

Part I: Software Engineering

2. “Testing Can Be Formal Too”: 30 Years Later, by  Marie-Claude Gaudel

3. A Short Visit to Distributed Computing Where Simplicity Is Considered a First-Class Property, by Michel Raynal

4. Modeling: From CASE Tools to SLE and Machine Learning, by Jean-Marc Jézéquel

5. At the Confluence of Software Engineering and Human-Computer Interaction: A Personal Account,  by Joëlle Coutaz

Part II:  Programming Language Mechanisms and Type Systems

6. From Procedures, Objects, Actors, Components, Services, to Agents, by  Jean-Pierre Briot

7. Semantics and Syntax, Between Computer Science and Mathematics, by Pierre-Louis Curien

8. Some Remarks About Dependent Type Theory, by Thierry Coquand

Part III: Theory

9. A Personal Historical Perspective on Abstract Interpretation, by Patrick Cousot

10. Tracking Redexes in the Lambda Calculus, by  Jean-Jacques Lévy

11. Confluence of Terminating Rewriting Computations, by  Jean-Pierre Jouannaud

Part IV: Language Design and Programming Methodology

12. Programming with Union, Intersection, and Negation Types, by Giuseppe Castagna

13, Right and Wrong: Ten Choices in Language Design, by Bertrand Meyer

What is the “French School of Programming”? As discussed in the Preface (although Jim Woodcock’s Foreword does not entirely agree) it is not anything defined in a formal sense, as the variety of approaches covered in the book amply demonstrates. What could be more different (for example) than Coq, OCaml (extensively referenced by several chapters) and Eiffel? Beyond the differences, however, there is a certain je ne sais quoi of commonality; to some extent, in fact, je sais quoi: reliance on mathematical principles, a constant quest for simplicity, a taste for elegance. It will be for the readers to judge.

Being single authors of their chapters, the authors felt free to share some of their deepest insights an thoughts. See for example Thierry Coquand’s discussion of the concepts that led to the widely successful Coq proof system, Marie-Claude Gaudel’s new look at her seminal testing work of 30 years ago, and Patrick Cousot’s detailed recounting of the intellectual path that led him and Radhia to invent abstract interpretation.

The French School of Programming
Edited by Bertrand Meyer
Springer, 2024. xxiv + 439 pages

Book page on Springer site
Amazon US page
Amazon France page
Amazon Germany page

The book is expensive (I tried hard to do something about it, and failed). But many readers should be able to download it, or individual chapters, for free through their institutions.

It was a privilege for me to take this project to completion and work with such extraordinary authors who produced such a collection of gems.

Maria Naumcheva, Sophie Ebersold, Alexandr Naumchev, Jean-Michel Bruel, Florian Galinier and Bertrand Meyer: Object-Oriented Requirements: a Unified Framework for Specifications, Scenarios and Tests, in JOT (Journal of Object Technology), vol. 22, no. 1, pages 1:1-19, 2023. Available here with link to PDF  (the journal is open-access).

From the abstract:

A paradox of requirements specifications as dominantly practiced in the industry is that they often claim to be object-oriented (OO) but largely rely on procedural (non-OO) techniques. Use cases and user stories describe functional flows, not object types.

To gain the benefits provided by object technology (such as extendibility, reusability, and reliability), requirements should instead take advantage of the same data abstraction concepts – classes, inheritance, information hiding – as OO design and OO programs.

Many people find use cases and user stories appealing because of the simplicity and practicality of the concepts. Can we reconcile requirements with object-oriented principles and get the best of both worlds?

This article proposes a unified framework. It shows that the concept of class is general enough to describe not only “object” in a narrow sense but also scenarios such as use cases and user stories and other important artifacts such as test cases and oracles. Having a single framework opens the way to requirements that enjoy the benefits of both approaches: like use cases and user stories, they reflect the practical views of stakeholders; like object-oriented requirements, they lend themselves to evolution and reuse.

The article builds in part on material from chapter 7 of my requirements book (Handbook of Requirements and Business Analysis, Springer).

Often,  “we do this and then we do that” is just a lazy way of stating “to do that, we must have achieved this.” The second form is more general than the first, since there may be many things you can “do” to achieve a certain condition.

The extra generality is welcome for software requirements, which should describe essential properties without over-specifying, in particular without prescribing a specific ordering of operations  when it is only one possible sequence among several, thereby restricting the flexibility of designers and implementers.

This matter of logical versus sequential constraints is at the heart of the distinction between scenario-based techniques — use cases, user stories… — and object-oriented requirements. This article analyzes the distinction. It is largely extracted from my recent textbook, the Handbook of Requirements and Business Analysis [1], which contains a more extensive discussion.

1. Scenarios versus OO

Scenario techniques, most significantly use cases and user stories, have become dominant in requirements. They obviously fill a need and are intuitive to many people. As a general requirement technique, however, they lack abstraction. Assessed against object-oriented requirements techniques, they suffer from the same limitations as procedural (pre-OO)  techniques against their OO competitors in the area of design and programming. The same arguments that make object technology subsume non-OO approaches in those areas transpose to requirements.

Scenario techniques describe system properties in terms of a particular sequence of interactions with the system. A staple example of a use case is ordering a product through an e-commerce site, going through a number of steps. In contrast, an OO specification presents a certain number of abstractions and operations on them, chracterized by their logical properties. This description may sound vague, so we move right away to examples.

2. Oh no, not stacks again

Yes, stacks. This example is rather computer-sciency so it is not meant to convince anyone but just to explain the ideas. (An example more similar to what we deal with in the requirements of industry projects is coming next.)

A stack is a LIFO (Last-In, First-Out) structure. You insert and remove elements at the same end.

Think of a stack of plates, where you can deposit one plate at a time, at the top, and retrieve one plate at a time, also at the top. We may call the two operations put and remove. Both are commands (often known under the alternative names push and pop). We will also use an integer query count giving the number of elements.

Assume we wanted to specify the behavior of a stack through use cases. Possible use cases (all starting with an empty stack) are:

/1/

put
put ; put
put ; put ; put        — etc.: any number of successive put (our stacks are not bounded)
put ; remove
put ; put ; remove
put ; put ; remove ; remove
put ; put ; remove ; remove ; put ; remove

We should also find a way to specify that the system does not support such use cases as

/2/

remove ; put

or even just

/3/

remove

We could keep writing such use cases forever — some expressing normal sequences of operations, others describing erroneous cases — without capturing the fundamental rule that at any stage, the number of put so far has to be no less than the number of remove.

A simple way to capture this basic requirement is through logical constraints, also known as contracts, relying on assertions: preconditions which state the conditions under which an operation is permitted, and postconditions which describe properties of its outcome. In the example we can state that:

• put has no precondition, and the postcondition

          count = old count + 1

using the old notation to refer to the value of an expression before the operation (here, the postcondition states that put increases count by one).

• remove has the precondition

count > 0

and the postcondition

count = old count – 1

since it is not possible to remove an element from an empty stack. More generally the LIFO discipline implies that we cannot remove more than we have put.(Such illegal usage sequences are sometimes called “misuse cases.”)

(There are other properties, but the ones just given suffice for this discussion.)

The specification states what can be done with stacks (and what cannot) at a sufficiently high level of abstraction to capture all possible use cases. It enables us to keep track of the value of count in the successive steps of a use case; it tells us for example that all the use cases under /1/ above observe the constraints: with count starting at 0, taking into account the postconditions of put and remove, the precondition of every operation will be satisfied prior to all of its calls. For /2/ and /3/ that is not the case, so we know that these use cases are incorrect.

Although this example covers a data structure, not  requirements in the general sense, it illustrates how logical constraints are more general than scenarios:

• Use cases, user stories and other  forms of scenario only describe specific instances of behavior.
• An OO model with contracts yields a more abstract specification, to which individual scenarios can be shown to conform, or not.

3. Avoiding premature ordering decisions

As the stack example illustrates, object-oriented specifications stay away from premature time-order decisions by focusing on object types (classes) and their operations (queries and commands), without making an early commitment to the order of executing these operations.

In the book, I use in several places a use-case example from one of the best books about use cases (along with Ivar Jacobson’s original one of course): Alistair Cockburn’s Writing Effective Use Cases (Pearson Education, 2001). A simplified form of the example is:

1. A reporting party who is aware of the event registers a loss to the insurance company.

2. A clerk receives and assigns claim to a claims agent.

3. The assigned claims adjuster:

3.1 Conducts an investigation.
3.2 Evaluates damages.
3.3 Sets reserves.
3.4 Negotiates the claim.
3.5 Resolves the claim and closes it.

(A reserve in the insurance business is an amount that an insurer, when receiving a claim, sets aside as to cover the financial liability that may result from the claim.)

As a specification, this scenario is trying to express useful things; for example, you must set reserves before starting to negotiate the claim. But it expresses them in the form of a strict sequence of operations, a temporal constraint which does not cover the wide range of legitimate scenarios. As in the stack example, describing a few such scenarios is helpful as part of requirements elicitation, but to specify the resulting requirements it is more effective to state the logical constraints.

Here is a sketch (in Eiffel) of how a class INSURANCE_CLAIM could specify them in the form of contracts. Note the use of require to introduce a precondition and ensure for postconditions.

class INSURANCE_CLAIM feature

        — Boolean queries (all with default value False):
    is_investigated, is_evaluated, is_reserved,is_agreed,is_imposed, is_resolved:

BOOLEAN

    investigate
                — Conduct investigation on validity of claim. Set is_investigated.
        deferred
        ensure
            is_investigated
        end

    evaluate
                — Assess monetary amount of damages.
        require
            is_investigated
        deferred
        ensure
            is_evaluated
            — Note: is_investigated still holds (see the invariant at the end of the class text).
        end

    set_reserve
                — Assess monetary amount of damages. Set is_reserved.
        require
            is_investigated
            — Note: we do not require is_evaluated.
        deferred
        ensure
            is_reserved
        end
 

    negotiate
                — Assess monetary amount of damages. Set is_agreed only if negotiation
                — leads to an agreement with the claim originator.
        require
                   is_reserved
is_evaluated                       
        deferred
        ensure
            is_reserved
            — See the invariant for is_evaluated and is_investigated.
        end

    impose (amount: INTEGER)
                — Determine amount of claim if negotiation fails. Set is_imposed.
        require
            not is_agreed
            is_reserved
        deferred
        ensure
            is_imposed
        end

    resolve
                — Finalize handling of claim. Set is_resolved.
        require
            is_agreed or is_imposed
        deferred
        ensure
            is_resolved
        end

invariant                    — “⇒” is logical implication.

is_evaluated ⇒ is_investigated
is_reserved  ⇒ is_evaluated
is_resolved ⇒ is_agreed or is_imposed
is_agreed ⇒ is_evaluated
is_imposed ⇒ is_evaluated
is_imposed ⇒ not is_agreed
                          — Hence, by laws of logic, is_agreed ⇒ not is_imposed

end

Notice the interplay between the preconditions, postconditions and class invariant, and the various boolean-valued queries they involve (is_investigated, is_evaluated, is_reserved…). You can specify a strict order of operations o₁, o₂ …, as in a use case, by having a sequence of assertions p_i such that operation o_i has the contract clauses require p_i and ensure p_i+1; but assertions also enable you to specify a much broader range of allowable orderings as all acceptable.
The class specification as given is only a first cut and leaves many aspects untouched. It will be important in practice, for example, to include a query payment describing the amount to be paid for the claim; then impose has the postcondition payment = amount, and negotiate sets a certain amount for payment.
Even in this simplified form, the specification includes a few concepts that the original use case left unspecified, in particular the notion of imposing a payment (through the command impose) if negotiation fails. Using a logical style typically uncovers such important questions and provides a framework for answering them, helping to achieve one of the principal goals of requirements engineering.

4. Logical constraints are more general than sequential orderings

The specific sequence of actions described in the original use case (“main success scenario”) is compatible with the logical constraints: you can check that in the sequence

investigate
evaluate
set_reserve
negotiate
resolve

the postcondition of each step implies the precondition of the next one (the first has no precondition). In other words, the temporal specification satisfies the logical one. But you can also see that prescribing this order is a case of overspecification: other orderings also satisfy the logical specification. It may be possible for example — subject to confirmation by Subject-Matter Experts — to change the order of evaluate and set_reserve, or to perform these two operations in parallel.

The specification does cover the fundamental sequencing constraints; for example, the pre- and postcondition combinations imply that investigation must come before evaluation and resolution must be preceded by either negotiation or imposition. But they avoid the non-essential constraints which, in the use case, were only an artifact of the sequential style of specification, not a true feature of the problem.

The logical style is also more conducive to conducting a fruitful dialogue with domain experts and stakeholders:

• With a focus on use cases, the typical question from a requirements engineer (business analyst) is “do you do A before doing B?” Often the answer will be contorted, as in “usually yes, but only if C, oh and sometimes we might start with B if D holds, or we might work on A and B in parallel…“, leading to vagueness and to more complicated requirements specifications.
• With logic-based specifications, the two fundamental question types are: “what conditions do you need before doing B?” and “does doing A ensure condition C?”. They force stakeholders to assess their own practices and specify precisely the relations between operations of interest.

5. What use for scenarios?

Use-cases and more generally scenarios, while more restrictive than logical specifications, remain important as complements to specifications. They serve as both input and output to more abstract requirements specifications (such as OO specifications with contracts):

• As input to requirements: initially at least, stakeholders and Subject-Matter Experts often find it intuitive to describe typical system interactions, and their own activities, in the form of scenarios. Collecting such scenarios is an invaluable requirements elicitation technique. The requirements engineer must remember that any such scenario is just one example walk through the system, and must abstract from these examples to derive general logical rules.
• As output from requirements: from an OO specification with its contracts, the requirements engineers can produce valid use cases. “Valid” means that the operation at every step satisfies the applicable precondition, as a consequence of the previous steps’ postconditions and of the class invariant. The requirements engineers can then submit these use cases to the SMEs and through them to stakeholders to confirm that they make sense, update the logical conditions if they do not (to rule out bad use cases), and check the results they are expected to produce.

6. Where do scenarios fit?

While many teams will prefer to write scenarios (for the purposes just described) in natural language, it is possible to go one step further and, in an object-oriented approach to requirements, gather scenarios in classes. But that point exceeds the scope of the present sketch. We will limit ourselves here to the core observation: logical constraints subsume sequential specifications; you can deduce the ltter from the former, but not the other way around; and focusing on abstract logical specifications leads to a better understanding of the requirements.

Reference

Bertrand Meyer: Handbook of Requirements and Business Analysis, Springer, 2022. See the book page with sample chapters and further material here.

(This article was first published on the Communications of the ACM blog.)

Li Huang (PhD student at SIT) will be presenting at an ISSRE workshop the paper Improving Counterexample Quality from Failed Program Verification, written with Manuel Oriol and me. One can find the text on arXiv here. (I will update this reference with the official publication link when I have it.)

The result being presented is part of a more general effort at combining proofs and tests (with other papers in the pipeline). The idea of treating proofs and tests as complementary rather than competing methods of software verification is an old pursuit of mine (which among other consequences resulted in the creation with Yuri Gurevich of the Tests and Proofs conference, which I see is continuing to run). A particular observation is that failure means a different thing for proofs and tests.

A failed test provides interesting information (in fact it is a successful proof — of incorrectness). A successful proof is, of course, also interesting (in principle it should be end of the story), whereas a successful test tells us very little. But in the practice of program proving the common occurrence is failure to prove a program element correct. You are typically left with no clue as to the source of the failure. In the AutoProof verification system for Eiffel, we are able to rely on the underlying technology (Boogie and Z3) to extract a counterexample which gives concrete evidence: as with a failed test, a programmer can in general quickly understand what is wrong.

In other words, the useless negative result of the bottom-left entry of the above picture can produce a useful result:

The general approach is the subject of another article but this one focuses on producing tests that are actually significant for the programmer. If you get very large values, you will not immediately be able to relate to them. Hence the need for a process of minimization, described in the article. The results on our examples are encouraging, making it possible to evidence the bug on very small integer values.

Reference

Li Huang, Bertrand Meyer and Manuel Oriol: Improving Counterexample Quality from Failed Program Verification, 6th International Workshop on Software Faults, October 2022. Preprint available on arXiv here. The program workshop is available here; the presentation is on Monday, 31 October, 15:55 CET (7:55 AM Los Angeles, 10:55 New York).

Short version: the full text of my Introduction to the Theory of Programming Languages book (second printing, 1991) is now available. This page has more details including the table of chapters, and a link to the PDF (3.3MB, 448 + xvi pages).

The book is a survey of methods for language description, particularly semantics (operational, translational, denotational, axiomatic, complementary) and also serves as an introduction to formal methods. Obviously it would be written differently today but it may still have its use.

A few days ago I released the Axiomatic Semantics chapter of the book, and the chapter introducing mathematical notations. It looked at the time that I could not easily  release the rest in a clean form, because it is impossible or very hard to use the original text-processing tools (troff and such). I could do it for these two chapters because I had converted them years ago for my software verification classes at ETH.

By perusing old files, however,  I realized that around the same time (early 2000s) I actually been able to produce PDF versions of the other chapters as well, even integrating corrections to errata  reported after publication. (How I managed to do it then I have no idea, but the result looks identical, save the corrections, to the printed version.)

The figures were missing from that reconstructed version (I think they had been produced with Brian Kernighan’s PIC graphical description language , which is even more forgotten today than troff), but I scanned them from a printed copy and reinserted them into the PDFs.

Some elements were missing from my earlier resurrection: front matter, preface, bibliography, index. I was able to reconstruct them from the original troff source using plain MS Word. The downside is that they are not hyperlinked; the index has the page numbers (which may be off by 1 or 2 in some cases because of reformatting) but not hyperlinks to the corresponding occurrences as we would expect for a new book. Also, I was not able to reconstruct the table of contents; there is only a chapter-level table of contents which, however, is hyperlinked (in other words, chapter titles link to the actual chapters). In the meantime I obtained the permission of the original publisher (Prentice Hall, now Pearson Education Inc.).

Here again is the page with the book’s description and the link to the PDF:

bertrandmeyer.com/ITPL

My book Object-Oriented Software Construction, 2nd edition (see the Wikipedia page) has become hard to get. There are various copies floating around the Web but they often use bad typography (wrong colors) and are unauthorized.

In response to numerous requests and in anticipation of the third edition I have been able to make it available electronically (with the explicit permission of the original publisher).

You can find the link on another page on this site. (In sharing or linking please use that page, not the URL of the actual PDF which might change.)

I hope having the text freely available proves useful.

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

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

Some of the work involves the AutoProof framework, under development at SIT (earlier at ETH), although other topics are also available, particularly in static analysis.

Compensation is attractive. Candidates must have the credentials to work in Switzerland (typically, citizenship or residence in Switzerland or the EU). Although we work in part remotely like everyone else these days, the positions are residential.

Interested candidates should send a CV and relevant documents or links (and any questions) to bm@sit.org.

There is a new paper out, several years in the making:

The Role of Formalism in System Requirements
Jean-Michel Bruel, Sophie Ebersold, Florian Galinier, Manuel Mazzara, Alexander Naumchev, Bertrand Meyer
Computing Surveys (ACM), vol. 54, no. 5, June 2021, pages 1-36
DOI: https://doi.org/10.1145/3448975
Preprint available here.

The authors are from the Schaffhausen Institute of Technology in Switzerland, the University of Toulouse in France and Innopolis University in Russia. We make up a cross-institutional (and unofficial) research group which has for several years now been working on improving the state of software requirements, with both an engineering perspective and an interest in taking advantage of formal methods.

The article follows this combined formal-informal approach by reviewing the principal formal methods in requirements but also taking into consideration non-formal ones — including techniques widely used in industry, such as DOORS — and studying how they can be used in a more systematic way. It uses a significant example (a “Landing Gear System” or LGS for aircraft) to compare them and includes extensive tables comparing the approaches along a number of systematic criteria.

Here is the abstract:

A major determinant of the quality of software systems is the quality of their requirements, which should be both understandable and precise. Most requirements are written in natural language, which is good for understandability but lacks precision.

To make requirements precise, researchers have for years advocated the use of mathematics-based notations and methods, known as “formal.” Many exist, differing in their style, scope, and applicability.

The present survey discusses some of the main formal approaches and compares them to informal methods.The analysis uses a set of nine complementary criteria, such as level of abstraction, tool availability, and traceability support. It classifies the approaches into five categories based on their principal style for specifying requirements: natural-language, semi-formal, automata/graphs, mathematical, and seamless (programming-language-based). It includes examples from all of these categories, altogether 21 different approaches, including for example SysML, Relax, Eiffel, Event-B, and Alloy.

The review discusses a number of open questions, including seamlessness, the role of tools and education, and how to make industrial applications benefit more from the contributions of formal approaches.

For me, of course, this work is the continuation of a long-running interest in requirements and specifications and how to express them using the tools of mathematics, starting with a 1985 paper, still being cited today, with a strikingly similar title: On Formalism in Specifications.

Trivia: the “response to referees” (there were no fewer than eight of them!) after the first review took up 85 pages. Maybe not for the Guinness Book, but definitely a personal record. (And an opportunity to thank the referees for detailed comments that considerably helped shape the final form of the paper.)

Correction (20 July 2021): I just noted that I had forgotten to list myself among the authors! Not a sign of modesty (I don’t have any), more of absent-mindedness. Now corrected.

Science progresses through people taking advantage of others’ insights and inventions. One of the conditions that makes the game possible is that you acknowledge what you take. For the originator, it is rewarding to see one’s ideas reused, but frustrating when that happens without acknowledgment, especially when you are yourself punctilious about citing your own sources of inspiration.

I have started to record some concepts that are widely known and applied today and which I believe I originated in whole or in part, whether or not their origin is cited by those who took them. The list below is not complete and I may update it in the future. It is not a list of ideas I contributed, only of those fulfilling two criteria:

• Others have built upon them.  (If there is an idea that I think is great but no one paid attention to it, the list does not include it.)
• They have gained wide visibility.

There is a narcissistic aspect to this exercise and if people want to dismiss it as just showing I am full of myself so be it. I am just a little tired of being given papers to referee that state that genericity was invented by Java, that no one ever thought of refactoring before agile methods, and so on. It is finally time to state some facts.

Facts indeed: I back every assertion by precise references. So if I am wrong — i.e. someone preceded me — the claims of precedence can be refuted; if so I will update or remove them. All articles by me cited in this note are available (as downloadable PDFs) on my publication page. (The page is up to date until 2018; I am in the process of adding newer publications.)

Post-publication note: I have started to receive some comments and added them in a Notes section at the end; references to those notes are in the format [A].

Final disclaimer (about the narcissistic aspect): the exercise of collecting such of that information was new for me, as I do not usually spend time reflecting on the past. I am much more interested in the future and definitely hope that my next contributions will eclipse any of the ones listed below.

Programming concepts: substitution principle

Far from me any wish to under-represent the seminal contributions of Barbara Liskov, particularly her invention of the concept of abstract data type on which so much relies. As far as I can tell, however, what has come to be known as the “Liskov Substitution Principle” is essentially contained in the discussion of polymorphism in section 10.1 of in the first edition (Prentice Hall, 1988) of my book Object-Oriented Software Construction (hereafter OOSC1); for example, “the type compatibility rule implies that the dynamic type is always a descendant of the static type” (10.1.7) and “if B inherits from A, the set of objects that can be associated at run time with an entity [generalization of variable] includes instances of B and its descendants”.

Perhaps most tellingly, a key aspect of the substitution principle, as listed for example in the Wikipedia entry, is the rule on assertions: in a proper descendant, keep the invariant, keep or weaken the precondition, keep or strengthen the postcondition. This rule was introduced in OOSC1, over several pages in section 11.1. There is also an extensive discussion in the article Eiffel: Applying the Principles of Object-Oriented Design published in the Journal of Systems and Software, May 1986.

The original 1988 Liskov article cited (for example) in the Wikipedia entry on the substitution principle says nothing about this and does not in fact include any of the terms “assertion”, “precondition”, “postcondition” or “invariant”. To me this absence means that the article misses a key property of substitution: that the abstract semantics remain the same. (Also cited is a 1994 Liskov article in TOPLAS, but that was many years after OOSC1 and other articles explaining substitution and the assertion rules.)

Liskov’s original paper states that “if for each object o1 of type S there is an object o2 of type T such that for all programs P defined in terms of T, the behavior of P is unchanged when o1 is substituted for oz, then S is a subtype of T.” As stated, this property is impossible to satisfy: if the behavior is identical, then the implementations are the same, and the two types are identical (or differ only by name). Of course the concrete behaviors are different: applying the operation rotate to two different figures o1 and o2, whose types are subtypes of FIGURE and in some cases of each other, will trigger different algorithms — different behaviors. Only with assertions (contracts) does the substitution idea make sense: the abstract behavior, as characterized by preconditions, postconditions and the class invariants, is the same (modulo respective weakening and strengthening to preserve the flexibility of the different version). Realizing this was a major step in understanding inheritance and typing.

I do not know of any earlier (or contemporary) exposition of this principle and it would be normal to get the appropriate recognition.

Software design: design patterns

Two of the important patterns in the “Gang of Four” Design Patterns book (GoF) by Gamma et al. (1995) are the Command Pattern and the Bridge Pattern. I introduced them (under different names) in the following publications:

• The command pattern appears in OOSC1 under the name “Undo-Redo” in section 12.2. The solution is essentially the same as in GoF. I do not know of any earlier exposition of the technique. See also notes [B] and [C].

• The bridge pattern appears under the name “handle technique” in my book Reusable Software: The Base Component Libraries (Prentice Hall, 1994). It had been described several years earlier in manuals for Eiffel libraries. I do not know of an earlier reference. (The second edition of Object-Oriented Software Construction — Prentice Hall, 1997, “OOSC2” –, which also describes it, states that a similar technique is described in an article by Josef Gil and Ricardo Szmit at the TOOLS USA conference in the summer of 1994, i.e. after the publication of Reusable Software.)

Note that it is pointless to claim precedence over GoF since that book explicitly states that it is collecting known “best practices”, not introducing new ones. The relevant questions are: who, pre-GoF, introduced each of these techniques first; and which publications does the GoF cites as “prior art”  for each pattern. In the cases at hand, Command and Bridge, it does not cite OOSC1.

To be concrete: unless someone can point to an earlier reference, then anytime anyone anywhere using an interactive system enters a few “CTRL-Z” to undo commands, possibly followed by some “CTRL-Y” to redo them (or uses other UI conventions to achieve these goals), the software most likely relying on a technique that I first described in the place mentioned above.

Software design: Open-Closed Principle

Another contribution of OOSC1 (1988), section 2.3, reinforced in OOSC2 (1997) is the Open-Closed principle, which explained one of the key aspects of inheritance: the ability to keep a module both closed (immediately usable as is) and open to extension (through inheritance, preserving the basic semantics. I am mentioning this idea only in passing since in this case my contribution is usually recognized, for example in the Wikipedia entry.

Software design: OO for reuse

Reusability: the Case for Object-Oriented Design (1987) is, I believe, the first publication that clearly explained why object-oriented concepts were (and still are today — in Grady Booch’s words, “there is no other game in town”) the best answer to realize the goal of software construction from software components. In particular, the article:

• Explains the relationship between abstract data types and OO programming, showing the former as the theoretical basis for the latter. (The CLU language at MIT originated from Liskov’s pioneering work on abstract data types, but was not OO in the full sense of the term, missing in particular a concept of inheritance.)
• Shows that reusability implies bottom-up development. (Top-down refinement was the mantra at the time, and promoting bottom-up was quite a shock for many people.)
• Explains the role of inheritance for reuse, as a complement to Parnas’s interface-based modular construction with information hiding.

Software design: Design by Contract

The contribution of Design by Contract is one that is widely acknowledged so I don’t have any point to establish here — I will just recall the essentials. The notion of assertion goes back to the work of Floyd, Hoare and Dijkstra in the sixties and seventies, and correctness-by-construction to Dijktra, Gries and Wirth, but Design by Contract is a comprehensive framework providing:

• The use of assertions in an object-oriented context. (The notion of class invariant was mentioned in a paper by Tony Hoare published back in 1972.)
• The connection of inheritance with assertions (as sketched above). That part as far as I know was entirely new.
• A design methodology for quality software: the core of DbC.
• Language constructs carefully seamed into the fabric of the language. (There were precedents there, but in the form of research languages such as Alphard, a paper design only, not implemented, and Euclid.)
• A documentation methodology.
• Support for testing.
• Support for a consistent theory of exception handling (see next).

Design by Contract is sometimes taken to mean simply the addition of a few assertions here and there. What the term actually denotes is a comprehensive methodology with all the above components, tightly integrated into the programming language. Note in particular that preconditions and postconditions are not sufficient; in an OO context class invariants are essential.

Software design: exceptions

Prior to the Design by Contract work, exceptions were defined very vaguely, as something special you do outside of “normal” cases, but without defining “normal”. Design by Contract brings a proper perspective by defining these concepts precisely. This was explained in a 1987 article, Disciplined Exceptions ([86] in the list), rejected by ECOOP but circulated as a technical report; they appear again in detail in OOSC1 (sections 7.10.3 to 7.10.5).

Other important foundational work on exceptions, to which I know no real precursor (as usual I would be happy to correct any omission), addressed what happens to the outcome of an exception in a concurrent or distributed context. This work was done at ETH, in particular in the PhD theses  of B. Morandi and A. Kolesnichenko, co-supervised with S. Nanz. See the co-authored papers [345] and [363].

On the verification aspect of exceptions, see below.

Software design: refactoring

I have never seen a discussion of refactoring that refers to the detailed discussion of generalization in both of the books Reusable Software (1994, chapter 3) and Object Success (Prentice Hall, 1995, from page 122 to the end of chapter 6). These discussions describe in detail how, once a program has been shown to work, it should be subject to a posteriori design improvements. It presents several of the refactoring techniques (as they were called when the idea gained traction several years later), such as moving common elements up in the class hierarchy, and adding an abstract class as parent to concrete classes ex post facto.

These ideas are an integral part of the design methodology presented in these books (and again in OOSC2 a few later). It is beyond me why people would present refactoring (or its history, as in the Wikipedia entry on the topic) without referring to these publications, which were widely circulated and are available for anyone to inspect.

Software design: built-in documentation and Single-Product principle

Another original contribution was the idea of including documentation in the code itself and relying on tools to extract the documentation-only information (leaving implementation elements aside). The idea, described in detail in OOSC1 in 1988 (sections 9.4 and 9.5) and already mentioned in the earlier Eiffel papers, is that code should be self-complete, containing elements of various levels of abstraction; some of them describe implementation, but the higher-level elements describe specification, and are distinguished syntactically in such a way that tools can extract them to produce documentation at any desired level of abstraction.

The ideas were later applied through such mechanisms as JavaDoc (with no credit as far as I know). They were present in Eiffel from the start and the underlying principles, in particular the “Single Product principle” (sometimes “Self-Documentation principle”, and also generalized by J. Ostroff and R. Paige as “Single-Model principle”). Eiffel is the best realization of these principles thanks to:

• Contracts (as mentioned above): the “contract view” of a class (called “short form” in earlier descriptions) removes the implementations but shows the relevant preconditions, postconditions and class invariants, given a precise and abstract specification of the class.
• Eiffel syntax has a special place for “header comments”, which describe high-level properties and remain in the contract view.
• Eiffel library class documentation has always been based on specifications automatically extracted from the actual text of the classes, guaranteeing adequacy of the documentation. Several formats are supported (including, from 1995 on, HTML, so that documentation can be automatically deployed on the Web).
• Starting with the EiffelCase tool in the early 90s, and today with the Diagram Tool of EiffelStudio, class structures (inheritance and client relationships) are displayed graphically, again in an automatically extracted form, using either the BON or UML conventions.

One of the core benefits of the Single-Product principle is to guard against what some of my publications called the “Dorian Gray” syndrome: divergence of an implementation from its description, a critical problem in software because of the ease of modifying stuff. Having the documentation as an integral part of the code helps ensure that when information at some level of abstraction (specification, design, implementation) changes, the other levels will be updated as well.

Crucial in the approach is the “roundtripping” requirement: specifiers or implementers can make changes in any of the views, and have them reflected automatically in the other views. For example, you can graphically draw an arrow between two bubbles representing classes B and A in the Diagram Tool, and the code of B will be updated with “inherit A”; or you can add this Inheritance clause textually in the code of class B, and the diagram will be automatically updated with an arrow.

It is important to note how contrarian and subversive these ideas were at the time of their introduction (and still to some extent today). The wisdom was that you do requirements then design then implementation, and that code is a lowly product entirely separate from specification and documentation. Model-Driven Development perpetuates this idea (you are not supposed to modify the code, and if you do there is generally no easy way to propagate the change to the model.) Rehabilitating the code (a precursor idea to agile methods, see below) was a complete change of perspective.

I am aware of no precedent for this Single Product approach. The closest earlier ideas I can think of are in Knuth’s introduction of Literate Programming in the early eighties (with a book in 1984). As in the Single-product approach, documentation is interspersed with code. But the literate programming approach is (as presented) top-down, with English-like explanations progressively being extended with implementation elements. The Single Product approach emphasizes the primacy of code and, in terms of the design process, is very much yoyo, alternating top-down (from the specification to the implementation) and bottom-up (from the implementation to the abstraction) steps. In addition, a large part of the documentation, and often the most important one, is not informal English but formal assertions. I knew about Literate Programming, of course, and learned from it, but Single-Product is something else.

Software design: from patterns to components

Karine Arnout’s thesis at ETH Zurich, resulting in two co-authored articles ([255] and [257], showed that contrary to conventional wisdom a good proportion of the classical design patterns, including some of the most sophisticated, can be transformed into reusable components (indeed part of an Eiffel library). The agent mechanism (see below) was instrumental in achieving that result.

Programming, design and specification concepts: abstract data types

Liskov’s and Zilles’s ground-breaking 1974 abstract data types paper presented the concepts without a mathematical specification, using programming language constructs instead. A 1976 paper (number [3] in my publication list, La Description des Structures de Données, i.e. the description of data structures) was as far as I know one of the first to present a mathematical formalism, as  used today in presentations of ADTs. John Guttag was taking a similar approach in his PhD thesis at about the same time, and went further in providing a sound mathematical foundation, introducing in particular (in a 1978 paper with Jim Horning) the notion of sufficient completeness, to which I devoted a full article in this blog  (Are My Requirements Complete?) about a year ago. My own article was published in a not very well known journal and in French, so I don’t think it had much direct influence. (My later books reused some of the material.)

The three-level description approach of that article (later presented in English for an ACM workshop in the US in 1981, Pingree Park, reference [28]) is not well known but still applicable, and would be useful to avoid frequent confusions between ADT specifications and more explicit descriptions.

When I wrote my 1976 paper, I was not aware of Guttag’s ongoing work (only of the Liskov and Zilles paper), so the use of a mathematical framework with functions and predicates on them was devised independently. (I remember being quite happy when I saw what the axioms should be for a queue.) Guttag and I both gave talks at a workshop organized by the French programming language interest group in 1977 and it was fun to see that our presentations were almost identical. I think my paper still reads well today (well, if you read French). Whether or not it exerted direct influence, I am proud that it independently introduced the modern way of thinking of abstract data types as characterized by mathematical functions and their formal (predicate calculus) properties.

Language mechanisms: genericity with inheritance

Every once in a while I get to referee a paper that starts “Generics, as introduced in Java…” Well, let’s get some perspective here. Eiffel from its introduction in 1985 combined genericity and inheritance. Initially, C++ users and designers claimed that genericity was not needed in an OO context and the language did not have it; then they introduced template. Initially, the designers of Java claimed (around 1995) that genericity was not needed, and the language did not have it; a few years later Java got generics. Initially, the designers of C# (around 1999) claimed that genericity was not needed, and the language did not have it; a few years later C# and .NET got generics.

Genericity existed before Eiffel of course; what was new was the combination with inheritance. I had been influenced by work on generic modules by a French researcher, Didier Bert, which I believe influenced the design of Ada as well; Ada was the language that brought genericity to a much broader audience than the somewhat confidential languages that had such a mechanism before. But Ada was not object-oriented (it only had modules, not classes). I was passionate about object-oriented programming (at a time when it was generally considered, by the few people who had heard of it as an esoteric, academic pursuit). I started — in the context of an advanced course I was teaching at UC Santa Barbara — an investigation of how the two mechanisms relate to each other. The results were a paper at the first OOPSLA in 1986, Genericity versus Inheritance, and the design of the Eiffel type system, with a class mechanism, inheritance (single and multiple), and genericity, carefully crafted to complement each other.

With the exception of a Trellis-Owl, a  design from Digital Equipment Corporation also presented at the same OOPSLA (which never gained significant usage), there were no other OO languages with both mechanisms for several years after the Genericity versus Inheritance paper and the implementation of genericity with inheritance in Eiffel available from 1986 on. Eiffel also introduced, as far as I know, the concept of constrained genericity, the second basic mechanism for combining genericity with inheritance, described in Eiffel: The Language (Prentice Hall, 1992, section 10.8) and discussed again in OOSC2 (section 16.4 and throughout). Similar mechanisms are present in many languages today.

It was not always so. I distinctly remember people bringing their friends to our booth at some conference in the early nineties, for the sole purpose of having a good laugh with them at our poster advertising genericity with inheritance. (“What is this thing they have and no one else does? Generi-sissy-tee? Hahaha.”). A few years later, proponents of Java were pontificating that no serious language needs generics.

It is undoubtedly part of of the cycle of invention (there is a Schopenhauer citation on this, actually the only thing from Schopenhauer’s philosophy that I ever understood [D]) that people at some point will laugh at you; if it did brighten their day, why would the inventor deny them one of the little pleasures of life? But in terms of who laughs last, along the way C++ got templates, Java got generics, C# finally did too, and nowadays all typed OO languages have something of the sort.

Language mechanisms: multiple inheritance

Some readers will probably have been told that multiple inheritance is a bad thing, and hence will not count it as a contribution, but if done properly it provides a major abstraction mechanism, useful in many circumstances. Eiffel showed how to do multiple inheritance right by clearly distinguishing between features (operations) and their names, defining a class as a finite mapping between names and features, and using renaming to resolve any name clashes.

Multiple inheritance was made possible by an implementation innovation: discovering a technique (widely imitated since, including in single-inheritance contexts) to implement dynamic binding in constant time. It was universally believed at the time that multiple inheritance had a strong impact on performance, because dynamic binding implied a run-time traversal of the class inheritance structure, already bad enough for single inheritance where the structure is a tree, but prohibitive with multiple inheritance for which it is a directed acyclic graph. From its very first implementation in 1986 Eiffel used what is today known as a virtual table technique which guarantees constant-time execution of routine (method) calls with dynamic binding.

Language mechanisms: safe GC through strong static typing

Simula 67 implementations did not have automatic garbage collection, and neither had implementations of C++. The official excuse in the C++ case was methodological: C programmers are used to exerting manual control of memory usage. But the real reason was a technical impossibility resulting from the design of the language: compatibility with C precludes the provision of a good GC.

More precisely, of a sound and complete GC. A GC is sound if it will only reclaim unreachable objects; it is complete if it will reclaim all unreachable objects. With a C-based language supporting casts (e.g. between integers and pointers) and pointer arithmetic, it is impossible to achieve soundness if we aim at a reasonable level of completeness: a pointer can masquerade as an integer, only to be cast back into a pointer later on, but in the meantime the garbage collector, not recognizing it as a pointer, may have wrongly reclaimed the corresponding object. Catastrophe.

It is only possible in such a language to have a conservative GC, meaning that it renounces completeness. A conservative GC will treat as a pointer any integer whose value could possibly be a pointer (because it lies between the bounds of the program’s data addresses in memory). Then, out of precaution, the GC will refrain from reclaiming the objects at these addresses even if they appear unreachable.

This approach makes the GC sound but it is only a heuristics, and it inevitably loses completeness: every once in a while it will fail to reclaim some dead (unreachable) objects around. The result is a program with memory leaks — usually unacceptable in practice, particularly for long-running or continuously running programs where the leaks inexorably accumulate until the program starts thrashing then runs out of memory.

Smalltalk, like Lisp, made garbage collection possible, but was not a typed language and missed on the performance benefits of treating simple values like integers as a non-OO language would. Although in this case I do not at the moment have a specific bibliographic reference, I believe that it is in the context of Eiffel that the close connection between strong static typing (avoiding mechanisms such as casts and pointer arithmetic) and the possibility of sound and complete garbage collection was first clearly explained. Explained in particular around 1990 in a meeting with some of the future designers of Java, which uses a similar approach, also taken over later on by C#.

By the way, no one will laugh at you today for considering garbage collection as a kind of basic human right for programmers, but for a long time the very idea was quite sulfurous, and advocating it subjected you to a lot of scorn. Here is an extract of the review I got when I submitted the first Eiffel paper to IEEE Transactions on Software Engineering:

Systems that do automatic garbage collection and prevent the designer from doing his own memory management are not good systems for industrial-strength software engineering.

Famous last words. Another gem from another reviewer of the same paper:

I think time will show that inheritance (section 1.5.3) is a terrible idea.

Wow! I wish the anonymous reviewers would tell us what they think today. Needless to say, the paper was summarily rejected. (It later appeared in the Journal of Systems and Software — as [82] in the publication list — thanks to the enlightened views of Robert Glass, the founding editor.)

Language mechanisms: void safety

Void safety is a property of a language design that guarantees the absence of the plague of null pointer dereferencing.

The original idea came (as far as I know) from work at Microsoft Research that led to the design of a research language called C-omega; the techniques were not transferred to a full-fledged programming language. Benefiting from the existence of this proof of concept, the Eiffel design was reworked to guarantee void safety, starting from my 2005 ECOOP keynote paper (Attached Types) and reaching full type safety a few years later. This property of the language was mechanically proved in a 2016 ETH thesis by A. Kogtenkov.

Today all significant Eiffel development produces void-safe code. As far as I know this was a first among production programming languages and Eiffel remains the only production language to provide a guarantee of full void-safety.

This mechanism, carefully crafted (hint: the difficult part is initialization), is among those of which I am proudest, because in the rest of the programming world null pointer dereferencing is a major plague, threatening at any moment to crash the execution of any program that uses pointers of references. For Eiffel users it is gone.

Language mechanisms: agents/delegates/lambdas

For a long time, OO programming languages did not have a mechanism for defining objects wrapping individual operations. Eiffel’s agent facility was the first such mechanism or among the very first together the roughly contemporaneous but initially much more limited delegates of C#. The 1999 paper From calls to agents (with P. Dubois, M. Howard, M. Schweitzer and E. Stapf, [196] in the list) was as far as I know the first description of such a construct in the scientific literature.

Language mechanisms: concurrency

The 1993 Communications of the ACM paper on Systematic Concurrent Object-Oriented Programming [136] was certainly not the first concurrency proposal for OO programming (there had been pioneering work reported in particular in the 1987 book edited by Tokoro and Yonezawa), but it innovated in offering a completely data-race-free model, still a rarity today (think for example of the multi-threading mechanisms of dominant OO languages).

SCOOP, as it came to be called, was implemented a few years later and is today a standard part of Eiffel.

Language mechanisms: selective exports

Information hiding, as introduced by Parnas in his two seminal 1972 articles, distinguishes between public and secret features of a module. The first OO programming language, Simula 67, had only these two possibilities for classes and so did Ada for modules.

In building libraries of reusable components I realized early on that we need a more fine-grained mechanism. For example if class LINKED_LIST uses an auxiliary class LINKABLE to represent individual cells of a linked list (each with a value field and a “right” field containing a reference to another LINKABLE), the features of LINKABLE (such as the operation to reattach the “right” field) should not be secret, since LINKED_LIST needs them; but they should also not be generally public, since we do not want arbitrary client objects to mess around with the internal structure of the list. They should be exported selectively to LINKED_LIST only. The Eiffel syntax is simple: declare these operations in a clause of the class labeled “feature {LINKED_LIST}”.

This mechanism, known as selective exports, was introduced around 1989 (it is specified in full in Eiffel: The Language, from 1992, but was in the Eiffel manuals earlier). I think it predated the C++ “friends” mechanism which serves a similar purpose (maybe someone with knowledge of the history of C++ has the exact date). Selective exports are more general than the friends facility and similar ones in other OO languages: specifying a class as a friend means it has access to all your internals. This solution is too coarse-grained. Eiffel’s selective exports make it possible to define the specific export rights of individual operations (including attributes/fields) individually.

Language mechanisms and implementation: serialization and schema evolution

I did not invent serialization. As a student at Stanford in 1974 I had the privilege, at the AI lab, of using SAIL (Stanford Artificial Intelligence Language). SAIL was not object-oriented but included many innovative ideas; it was far ahead of its time, especially in terms of the integration of the language with (what was not yet called) its IDE. One feature of SAIL with which one could fall in love at first sight was the possibility of selecting an object and having its full dependent data structure (the entire subgraph of the object graph reached by following references from the object, recursively) stored into a file, for retrieval at the next section. After that, I never wanted again to live without such a facility, but no other language and environment had it.

Serialization was almost the first thing we implemented for Eiffel: the ability to write object.store (file) to have the entire structure from object stored into file, and the corresponding retrieval operation. OOSC1 (section 15.5) presents these mechanisms. Simula and (I think) C++ did not have anything of the sort; I am not sure about Smalltalk. Later on, of course, serialization mechanisms became a frequent component of OO environments.

Eiffel remained innovative by tackling the difficult problems: what happens when you try to retrieve an object structure and some classes have changed? Only with a coherent theoretical framework as provided in Eiffel by Design by Contract can one devise a meaningful solution. The problem and our solutions are described in detail in OOSC2 (the whole of chapter 31, particularly the section entitled “Schema evolution”). Further advances were made by Marco Piccioni in his PhD thesis at ETH and published in joint papers with him and M. Oriol, particularly [352].

Language mechanisms and implementation: safe GC through strong static typing

Simula 67 (if I remember right) did not have automatic garbage collection, and neither had C++ implementations. The official justification in the case of C++ was methodological: C programmers are used to exerting manual control of memory usage. But the real obstacle was technical: compatibility with C makes it impossible to have a good GC. More precisely, to have a sound and complete GC. A GC is sound if it will only reclaim unreachable objects; it is complete if it will reclaim all unreachable objects. With a C-based language supporting casts (e.g. between integers and pointers) and pointer arithmetic, it is impossible to achieve soundness if we aim at a reasonable level of completeness: a pointer can masquerade as an integer, only to be cast back into a pointer later on, but in the meantime the garbage collector, not recognizing it as a pointer, may have wrongly reclaimed the corresponding object. Catastrophe. It is only possible in such a language to have a conservative GC, which will treat as a pointer any integer whose value could possibly be a pointer (because its value lies between the bounds of the program’s data addresses in memory). Then, out of precaution, it will not reclaim the objects at the corresponding address. This approach makes the GC sound but it is only a heuristics, and it may be over-conservative at times, wrongly leaving dead (i.e. unreachable) objects around. The result is, inevitably, a program with memory leaks — usually unacceptable in practice.

Smalltalk, like Lisp, made garbage collection possible, but was not a typed language and missed on the performance benefits of treating simple values like integers as a non-OO language would. Although in this case I do not at the moment have a specific bibliographic reference, I believe that it is in the context of Eiffel that the close connection between strong static typing (avoiding mechanisms such as casts and pointer arithmetic) and the possibility of sound and complete garbage collection was first clearly explained. Explained in particular to some of the future designers of Java, which uses a similar approach, also taken over later on by C#.

By the way, no one will laugh at you today for considering garbage collection as a kind of basic human right for programmers, but for a long time it was quite sulfurous. Here is an extract of the review I got when I submitted the first Eiffel paper to IEEE <em>Transactions on Software Engineering:

Software engineering: primacy of code

Agile methods are widely and properly lauded for emphasizing the central role of code, against designs and other non-executable artifacts. By reading the agile literature you might be forgiven for believing that no one brought up that point before.

Object Success (1995) makes the argument very clearly. For example, chapter 3, page 43:

Code is to our industry what bread is to a baker and books to a writer. But with the waterfall code only appears late in the process; for a manager this is an unacceptable risk factor. Anyone with practical experience in software development knows how many things can go wrong once you get down to code: a brilliant design idea whose implementation turns out to require tens of megabytes of space or minutes of response time; beautiful bubbles and arrows that cannot be implemented; an operating system update, crucial to the project which comes five weeks late; an obscure bug that takes ages to be fixed. Unless you start coding early in the process, you will not be able to control your project.

Such discourse was subversive at the time; the wisdom in software engineering was that you need to specify and design a system to death before you even start coding (otherwise you are just a messy “hacker” in the sense this word had at the time). No one else in respectable software engineering circles was, as far as I know, pushing for putting code at the center, the way the above extract does.

Several years later, agile authors started making similar arguments, but I don’t know why they never referenced this earlier exposition, which still today I find not too bad. (Maybe they decided it was more effective to have a foil, the scorned Waterfall, and to claim that everyone else before was downplaying the importance of code, but that was not in fact everyone.)

Just to be clear, Agile brought many important ideas that my publications did not anticipate; but this particular one I did.

Software engineering: the roles of managers

Extreme Programming and Scrum have brought new light on the role of managers in software development. Their contributions have been important and influential, but here too they were for a significant part prefigured by a long discussion, altogether two chapters, in Object Success (1995).

To realize this, it is enough to read the titles of some of the sections in those chapters, describing roles for managers (some universal, some for a technical manager): “risk manager”, “interface with the rest of the world” (very scrummy!), “protector of the team’s sanity”, “method enforcer” (think Scrum Master), “mentor and critic”. Again, as far as I know, these were original thoughts at the time; the software engineering literature for the most part did not talk about these issues.

Software engineering: outsourcing

As far as I know the 2006 paper Offshore Development: The Unspoken Revolution in Software Engineering was the first to draw attention, in the software engineering community, to the peculiar software engineering challenges of distributed and outsourced development.

Software engineering: automatic testing

The AutoTest project (with many publications, involving I. Ciupa, A. Leitner, Y. Wei, M. Oriol, Y. Pei, M. Nordio and others) was not the first to generate tests automatically by creating numerous instances of objects and calling applicable operations (it was preceded by Korat at MIT), but it was the first one to apply this concept with Design by Contract mechanisms (without which it is of little practical value, since one must still produce test oracles manually) and the first to be integrated in a production environment (EiffelStudio).

Software engineering: make-less system building

One of the very first decisions in the design of Eiffel was to get rid of Make files.

Feldman’s Make had of course been a great innovation. Before Make, programmers had to produce executable systems manually by executing sequences of commands to compile and link the various source components. Make enabled them to instead  to define dependencies between components in a declarative way, resulting in a partial order, and then performed a topological sort to produce the sequence of comments. But preparing the list of dependencies remains a tedious task, particularly error-prone for large systems.

I decided right away in the design of Eiffel that we would never force programmers to write such dependencies: they would be automatically extracted from the code, through an exhaustive analysis of the dependencies between modules. This idea was present from the very the first Eiffel report in 1985 (reference [55] in the publication list): Eiffel programmers never need to write a Make file or equivalent (other than for non-Eiffel code, e.g. C or C++, that they want to integrate); they just click a Compile button and the compiler figures out the steps.

Behind this approach was a detailed theoretical analysis of possible relations between modules in software development (in many programming languages), published as the “Software Knowledge Base” at ICSE in 1985. That analysis was also quite instructive and I would like to return to this work and expand it.

Educational techniques: objects first

Towards an Object-Oriented Curriculum ( TOOLS conference, August 1993, see also the shorter JOOP paper in May of the same year) makes a carefully argued case for what was later called the Objects First approach to teaching programming. I would be interested to know if there are earlier publications advocating starting programming education with an OO language.

The article also advocated for the “inverted curriculum”, a term borrowed from work by Bernie Cohen about teaching electrical engineering. It was the first transposition of this concept to software education. In the article’s approach, students are given program components to use, then little by little discover how they are made. This technique met with some skepticism and resistance since the standard approach was to start from the very basics (write trivial programs), then move up. Today, of course, many introductory programming courses similarly provide students from day one with a full-fledged set of components enabling them to produce significant programs.

More recent articles on similar topics, taking advantage of actual teaching experience, are The Outside-In Method of Teaching Programming (2003) and The Inverted Curriculum in Practice (at ICSE 2006, with Michela Pedroni). The culmination of that experience is the textbook Touch of Class from 2009.

Educational techniques: Distributed Software Projects

I believe our team at ETH Zurich (including among others M. Nordio, J. Tschannen, P. Kolb and C. Estler and in collaboration with C. Ghezzi, E. Di Nitto and G. Tamburrelli at Politecnico di Milano, N. Aguirre at Rio Cuarto and many others in various universities) was the first to devise,  practice and document on a large scale (see publications and other details here) the idea of an educational software project conducted in common by student groups from different universities. It yielded a wealth of information on distributed software development and educational issues.

Educational techniques: Web-based programming exercises

There are today a number of cloud-based environments supporting the teaching of programming by enabling students to compile and test their programs on the Web, benefiting from a prepared environment (so that they don’t have to download any tools or prepare control files) and providing feedback. One of the first — I am not sure about absolute precedence — and still a leading one, used by many universities and applicable to many programming languages, is Codeboard.

The main developer, in my chair at ETH Zurich, was Christian Estler, supported in particular by M. Nordio and M. Piccioni, so I am only claiming a supporting role here.

Educational techniques: key CS/SE concepts

The 2001 paper Software Engineering in the Academy did a good job, I think, of defining the essential concepts to teach in a proper curriculum (part of what Jeannette Wing’s 2006 paper called Computational Thinking).

Program verification: agents (delegates etc.)

Reasoning about Function Objects (ICSE 2010, with M. Nordio, P. Müller and J. Tschannen) introduced verification techniques for objects representing functions (such as agents, delegates etc., see above) in an OO language. Not sure whether there were any such techniques before.

Specification languages: Z

The Z specification language has been widely used for formal development, particularly in the UK. It is the design of J-R Abrial. I may point out that I was a coauthor of the first publication on Z in English (1980),  describing a version that preceded the adaptation to a more graphical-style notation done later at Oxford. The first ever published description of Z, pertaining to an even earlier version, was in French, in my book Méthodes de Programmation (with C. Baudoin), Eyrolles, 1978, running over 15 pages (526-541), with the precise description of a refinement process.

Program verification: exceptions

Largely coming out of the PhD thesis of Martin Nordio, A Sound and Complete Program Logic for Eiffel (TOOLS 2009) introduces rules for dealing with exceptions in a Hoare-style verification framework.

Program verification: full library, and AutoProof

Nadia Polikarpova’s thesis at ETH, aided by the work of Carlo Furia and Julian Tschannen (they were the major contributors and my participation was less important), was as far as I know the first to produce a full functional verification of an actual production-quality reusable library. The library is EiffelBase 2, covering fundamental data structures.

AutoProof — available today, as a still experimental tool, through its Web interface, see here — relied on the AutoProof prover, built by the same team, and itself based on Microsoft Research’s Boogie and Z3 engines.

More

There are more concepts worthy of being included here, but for today I will stop here.

Notes

[A] One point of divergence between usual presentations of the substitution principle and the view in OOSC and my other publications is the covariance versus contravariance of routine argument types. It reflects a difference of views as to what the proper policy (both mathematically sound and practically usable) should be.

[B]  The GoF book does not cite OOSC for the command or bridge patterns. For the command pattern it cites (thanks to Adam Kosmaczewski for digging up the GoF text!) a 1985 SIGGRAPH paper by Henry Lieberman (There’s More to Menu Systems than Meets the Screen). Lieberman’s paper describes the notion of command object and mentions undoing in passing, but does not include the key elements of the command pattern (as explained in full in OOSC1), i.e. an abstract (deferred) command class with deferred procedures called (say) do_it and undo_it, then specific classes for each kind of command, each providing a specific implementation of those procedures, then a history list of commands supporting multiple-level undo and redo as explained in OOSC1. (Reading Lieberman’s paper with a 2021 perspective shows that it came tantalizingly close to the command pattern, but doesn’t get to it. The paper does talk about inheritance between command classes, but only to “define new commands as extensions to old commands”, not in the sense of a general template that can be implemented in many specific ways. And it does mention a list of objects kept around to enable recovery from accidental deletions, and states that the application can control its length, as is the case with a history list; but the objects in the list are not command objects, they are graphical and other objects that have been deleted.)

[C] Additional note on the command pattern: I vaguely remember seeing something similar to the OOSC1 technique in an article from a supplementary volume of the OOPSLA proceedings in the late eighties or early nineties, i.e. at the same time or slightly later, possibly from authors from Xerox PARC, but I have lost the reference.

[D] Correction: I just checked the source and learned that the actual Schopenhauer quote (as opposed to the one that is usually quoted) is different; it does not include the part about laughing. So much for my attempts at understanding philosophy.

If you want to know whether your_string has at least one upper-case character, you will write this in Eiffel:

if  ∃ c: your_string ¦ c.is_upper then …

Such predicate-calculus boolean expressions, using a quantifier ∀ (“for all”) or ∃ (“there exists”) are becoming common in Eiffel code. They are particularly useful in Design by Contract assertions, making it possible to characterize deep semantic properties of the code and its data structures. For example a class invariant clause in a class I wrote recently states

from_lists_exist: ∀ tf: triples_from ¦ tf ≠ Void                        — [1]

meaning that all the elements, if any, of the list triples_from  are non-void (non-null). The notation is the exact one from mathematics. (Mathematical notation sometimes uses a dot in place of the bar, but the bar is clearer, particularly in an OO context where the dot has another use.)

Programming languages should support time-honored notations from mathematics. Reaching this goal has been a driving force in the evolution of Eiffel, but not as a concession to “featurism” (the gratuitous piling up of language feature upon feature). The language must remain simple and consistent; any new feature must find its logical place in the overall edifice.

The design of programming languages is a constant search for the right balance between rigor, simplicity, consistency, formal understanding, preservation of existing code, innovation and expressiveness. The design of Eiffel has understood the last of these criteria as implying support for established notations from mathematics, not through feature accumulation but by re-interpreting these notations in terms of the language’s fundamental concepts. A typical example is the re-interpretation of the standard mathematical notation a + b as as simply an operator-based form for the object-oriented call a.plus (b), obtained by declaring “+” as an operator alias for the function plus in the relevant classes. There are many more such cases in today’s Eiffel. Quantifier expressions using ∀ and ∃ are the latest example.

 They are not a one-of-a-kind trick but just as a different syntax form for loops. Expressed in a more verbose form, the only one previously available, [1] would be:

across triples_from is tf all tf /= Void end                         — [2]

It is interesting to walk back the history further. [2] is itself a simplification of

across triples_from as tf all tf.item /= Void end               — [3]

where the “.item” has a good reason for being there, but that reason is irrelevant to a beginner. The earlier use of as in [3] is also the reason for the seemingly bizarre use of is in [2], which is only explainable by the backward compatibility criterion (code exists that uses as , which has a slightly different semantics from is), and will go away. But a few years ago the across loop variant did not exist and you would have had to write the above boolean expressions as

all_non_void (triples_from)

after defining a function

all_non_void (l: LIST [T]): BOOLEAN                                    — [4]
                         — Are all the elements of `l’, if any, non-void?
          local
pos: INTEGER
do
from
pos := l.index
l.start
Result := True
until not Result or l.after loop
l.forth
end
go_ith (pos)
end

The road traveled from [4] to [1] is staggering. As we introduced new notations in the history of Eiffel the reaction of the user community has sometimes been between cautious and negative. With the exception of a couple of quickly discarded ideas (such as the infamous and short-lived “!!” for creation), they were generally adopted widely because they simplify people’s life without adding undue complexity to the language. The key has been to avoid featurism and choose instead to provide two kinds of innovation:

• Major conceptual additions, which elevate the level of abstraction of the language. A typical introduction was the introduction of agents, which provide the full power of functional programming in an object-oriented context; another was the SCOOP concurrency mechanism. There have been only a few such extensions, all essential.
• Syntactical variants for existing concepts, allowing more concise forms obtained from traditional mathematical notation. The use of quantifier expressions as in [1] is the latest example.

Complaints of featurism still occasionally happen when people first encounter the new facilities, but they fade away quickly as people start using them. After writing a few expressions such as [1], no one wants to go back to any of the other forms.

These quantifier expressions using ∀ and ∃, as well as the “≠” not-equal sign for what used to be (and still commonly is) written “/=”, rely on Unicode. Eiffel started out when ASCII was the law of the land. (Or 8-bit extended ASCII, which does not help much since the extensions are rendered differently in different locales, i.e. the same 8-bit character code may mean something different on French and Swedish texts.) In recent years, Eiffel has made a quiet transition to full Unicode support. (Such support extends to manifest strings and operators, not to identifiers. The decision, which could be revisited, has been to keep the ASCII-only  policy for identifiers to favor compatible use by programmers regardless of their mother tongues.) The use of Unicode considerably extends the expressive power of the language, in particular for scientific software which can — thanks to Eiffel’s mechanism for defining free operators — rely on advanced mathematical notations.

Unicode is great, but I hear the question: how in the world can we enter the corresponding symbols, since our keyboards are still ASCII plus some extensions?

It would be tedious to have to select from a list of special symbols (as you do when inserting a mathematical symbol in Microsoft Word or, for that matter, as I did when inserting the phrase “∀ and ∃” in the preceding paragraph using WordPress).

The answer lies in the interplay between the language and the development environment. EiffelStudio, like other modern IDEs, includes an automatic completion mechanism which lets you enter the beginning of a construct and will take care of filling in the rest. Already useful for complex structures (if you type “if” the tools will create the entire “if … then … else … end” conditional structure for you to fill in), automatic completion will take care of inserting the appropriate Unicode symbols for you. Type for example “across”,  then CTRL-Space to trigger completion, and the choices will include the “∀” and “∃” forms. You can see below how this works:

Programming languages can be at the same time simple, easy to learn, consistent, and expressive. Start using quantifiers now!

Acknowledgments to the Ecma Technical Committee on Eiffel and the Eiffel Software team, particularly Alexander Kogtenkov (see his blog post here) and (for the completion mechanism and its animated illustration above) Jocelyn Fiat.

I have started a new series of video lectures, which I call “Meyer’s Object-Oriented Classes” (MOOC). The goal is to share insights I have gained over the years on various aspects of programming and software engineering. Many presentations are focused on one area, such as coding, design, analysis, theoretical computer science (even there you find a division between “Theory A”, i.e. complexity, Turing machines and the like, and “Theory B”, i.e. semantics, type theory etc.), software project management, concurrency… I have an interest in all and try to explain connections.

The first lecture describes the edit distance (Levenshtein) algorithm, explains its correctness by introducing the loop invariant, expands on that notion, then shows a recursive version, explores the connection with the original version (it’s the invariant), and probes further into another view of recursive computations, leading to the concept of dynamic programming.

The videos are on YouTube and can be accessed from bertrandmeyer.com/levenshtein. (The general page for all lectures is at bertrandmeyer.com/mooc.)

The lecture is recorded in four segments of about 15 minutes each. In the future I will limit myself to 8-10 minutes. In fact I may record this lecture again; for example it would be better if I had a live audience rather than talking to my screen, and in general the recording is somewhat low-tech, but circumstances command. Also, I will correct a few hiccups (at some point in the recording I notice a typo on a slide and fix it on the fly), but the content will remain the same.

Feedback is of course welcome. I hope to record about a lecture a week from now on.

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

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

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

1. Introduction and attempt #1

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

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

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

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

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

from

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

until i = j loop

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

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

end

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

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

First question: what is this program trying to do?

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

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

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

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

Notes to section 1

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

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

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

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

2. Attempt #2

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

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

t = [0   0]

The successive values of the variables and expressions are:

                                            m       i          j            i + j + 1

After initialization:                   1         2                3

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

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

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

We are now ready for the second attempt:

—  Program attempt #2.

from

i := 1 ; j := n

until i = j or Result > 0  loop

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

if t [m] ≤ x then

i := m  + 1

elseif t [m] = x then

Result := m

else                         — In this case t [m] > x

j := m – 1

end

end

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

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

3. Attempt #3

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

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

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

—  Program attempt #3.

from

i := 1 ; j := n

until i = j loop

m := (i + j + 1) // 2

if t [m] ≤ x then

i := m  + 1

else

j := m

end

end

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

What about this one?

3. Attempt #4 (also includes 3′)

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

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

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

                                                  m          i          j            i + j + 1

After initialization:                            1        2           4

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

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

Oops!

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

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

—  Program attempt #4.

from

i := 0 ; j := n + 1

until i = j loop

m := (i + j) // 2

if t [m] ≤ x then

i := m  + 1

else

j := m

end

end

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

5. Attempt #5

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

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

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

                                                 m          i          j            i + j

After initialization:                           0        3           3

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

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

i = j, exit loop

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

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

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

—  Program attempt #5.

from

i := 1 ; j := n + 1

until i ≥ j or Result > 0 loop

m := (i + j) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

Does it work now?

6. Attempt #6

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

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

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

(i + j) // 2

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

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

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

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

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

i + (j – i) // 2

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

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

—  Program attempt #6.

from

i := 1 ; j := n + 1

until i ≥ j or Result > 0 loop

m := i + (j – i) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

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

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

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

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

References for section 6

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

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

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

7. Using a program prover

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

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

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

We need a proof.

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

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

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

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

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

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

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

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

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

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

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

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

from

low := 0 ; up := n

until low ≥ up or Result > 0 loop

middle := low + ((up – low) // 2)

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

low := middle + 1

elseif  a [middle] > value then

up := middle

else

Result := middle

end

end

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

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

Note and references for section 7

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

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

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

8. Understanding the proof

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

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

from

i := 1 ; j := n + 1

until i ≥ j or Result > 0 loop

m := i + (j – i) // 2

if t [m] < x then

i := m + 1

elseif  t [m] > x then

j := m

else

Result := m

end

end

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

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

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

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

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

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

i ≥ j or Result > 0

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

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

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

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

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

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

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

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

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

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

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

if t [m] ≤ x then

i := m + 1

else

j := m

end

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

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

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

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

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

References and notes for section 8

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

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

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

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

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

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

9. Lessons learned

What was this journey about?

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

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

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

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

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

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

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

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

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

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

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

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

An invariant should be:

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

In the example:

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

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

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

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

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

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

References

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

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

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

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

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

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

Consider the following expression:

∃ c: s   ¦   moisture (c) = soft

This is obviously mathematics. To express such a property in a programming language, you have to write a function containing a loop that iterates through the elements of s. Right?

Wrong. The above construct is valid Eiffel. It’s a consequence of recent syntax extensions that retain all the simplicity and consistency of the language but take full advantage of Unicode. Of course you do not have Unicode characters such as ∃ on you keyboard, but EiffelStudio’s completion mechanism inserts them for you.

To see how this works, just read Alexander Kogtenkov’s recent blog post on the topic.

Note added 24 December 2020: you will find a longer exposition in a later article on this blog.

(Originally published on CACM blog.)

Most of the world programs in a very strange way. Strange to me. I usually hear the reverse question: people ask us, the Eiffel community, to explain why we program our way. I hardly understand the question, because the only mystery is how anyone can even program in any other way.

The natural reference is the beginning of One Flew Over the Cuckoo’s Nest: when entering an insane asylum and wondering who is an inmate and who a doctor, you may feel at a loss for objective criteria. Maybe the rest of the world is right and we are the nut cases. Common sense suggests it.

But sometimes one can go beyond common sense and examine the evidence. So lend me an ear while I explain my latest class invariant. Here it is, in Figure 1. (Wait, do not just run away yet.)

Figure 1: From the invariant of class MULTIGRAPH

This is a program in progress and by the time you read this note the invariant and enclosing class will have changed. But the ideas will remain.

Context: multigraphs

The class is called MULTIGRAPH and describes a generalized notion of graph, illustrated in Figure 2. The differences are that: there can be more than one edge between two nodes, as long as they have different tags (like the spouse and boss edges between 1 and 2); and there can be more than one edge coming out of a given node and with a given tag (such as the two boss edges out of 1, reflecting that 1’s boss might be 2 in some cases and 3 in others). Some of the nodes, just 1 here, are “roots”.

The class implements the notion of multigraph and provides a wide range of operations on multigraphs.

Figure 2: A multigraph

Data structures

Now we turn to the programming and software engineering aspects. I am playing with various ways of accessing multigraphs. For the basic representation of a multigraph, I have chosen a table of triples:

                triples_table: HASH_TABLE [TRIPLE, TUPLE [source: INTEGER; tag: INTEGER; target: INTEGER]]  — Table of triples, each retrievable through its `source’, `tag’ and `target’.

where the class TRIPLE describes [source, tag, target] triples, with a few other properties, so they are not just tuples. It is convenient to use a hash table, where the key is such a 3-tuple. (In an earlier version I used just an ARRAY [TRIPLE], but a hash table proved more flexible.)

Sources and targets are nodes, also called “objects”; we represent both objects and tags by integers for efficiency. It is easy to have structures that map symbolic tag names such as “boss” to integers.

triples_table is the core data structure but it turns out that for the many needed operations it is convenient to have others. This technique is standard: for efficiency, provide different structures to access and manipulate the same underlying information, with some redundancy. So I also have:

 triples_from:  ARRAYED_LIST [LIST [TRIPLE]]
               — Triples starting from a given object. Indexed by object numbers.

  triples_with:  HASH_TABLE [LIST [TRIPLE], INTEGER]
               — Triples labeled by a given tag. Key is tag number.

 triples_to:  ARRAYED_LIST [LIST [TRIPLE]]
               — Triples leading into a given object. Indexed by object numbers.

Figure 3 illustrates triples_from and Figures 4 illustrates triples_with. triples_to is similar.

Figure 3: The triples_from array of lists and the triples_table

Figure 4: The triples_with array of lists and the triples_table

It is also useful to access multigraphs through yet another structure, which gives us the targets associated with a given object and tag:

successors: ARRAY [HASH_TABLE [LIST [TRIPLE], INTEGER]]
               — successors [obj] [t] includes all o such that there is a t- reference from obj to o.

For example in Figure 1 successors [1] [spouse] is {2, 3}, and in Figures 3 and 4 successors [26] [t] is {22, 55, 57}. Of course we can obtain the “successors” information through the previously defined structures, but since this is a frequently needed operation I decided to include a specific data structure (implying that every operation modifying the multigraph must update it). I can change my mind later on and decide to make “successors” a function rather than a data structure; it is part of the beauty of OO programming, particularly in Eiffel, that such changes are smooth and hardly impact client classes.

There is similar redundancy in representing roots:

                roots:  LINKED_SET [INTEGER]
                              — Objects that are roots.

                is_root:  ARRAY [BOOLEAN]
                              — Which objects are roots? Indexed by object numbers.

If o is a root, then it appears in the “roots” set and is_root [o] has value True.

Getting things right

These are my data structures. Providing such a variety of access modes is a common programming technique. From a software engineering perspective ― specification, implementation, verification… ― it courts disaster. How do we maintain their consistency? It is very easy for a small mistake to slip into an operation modifying the graph, causing one of the data structures to be improperly updated, but in a subtle and rare enough way that it will not manifest itself during testing, coming back later to cause strange behavior that will be very hard to debug.

For example, one of the reasons I have a class TRIPLE and not just 3-tuples is that a triple is not exactly  the same as an edge in the multigraph. I have decided that by default the operation that removes and edge would not remove the corresponding triple from the data structure, but leave it in and mark it as “inoperative” (so class TRIPLE has an extra “is_inoperative” boolean field). There is an explicit GC-like mechanism to clean up deleted edges occasionally. This approach brings efficiency but makes the setup more delicate since we have to be extremely careful about what a triple means and what removal means.

This is where I stop understanding how the rest of the world can work at all. Without some rigorous tools I just do not see how one can get such things right. Well, sure, spend weeks of trying out test cases, printing out the structures, manually check everything (in the testing world this is known as writing lots of “oracles”), try at great pains to find out the reason for wrong results, guess what program change will fix the problem, and start again. Stop when things look OK. When, as Tony Hoare once wrote, there are no obvious errors left.

Setting aside the minuscule share of projects (typically in embedded life-critical systems) that use some kind of formal verification, this process is what everyone practices. One can only marvel that systems, including many successful ones, get produced at all. To take an analogy from another discipline, this does not compare to working like an electrical engineer. It amounts to working like an electrician.

For a short time I programmed like that too (one has to start somewhere, and programming methodology was not taught back then). I no longer could today. Continuing with the Hoare citation, the only acceptable situation is to stop when there are obviously no errors left.

How? Certainly not, in my case, by always being right the first time. I make mistakes like everyone else does. But I have the methodology and tools to avoid some, and, for those that do slip through, to spot and fix them quickly.

Help is available

First, the type system. Lots of inconsistencies, some small and some huge, which in an untyped language would only hit during execution, do not make it past compilation. We are not just talking here about using REAL instead of INTEGER. With a sophisticated type system involving multiple inheritance, genericity, information hiding and void safety, a compiler error message can reflect a tricky logical mistake. You are using a SET as if it were a LIST (some operations are common, but others not). You are calling an operation on a reference that may be void (null) at run time. And so on.

By the way, about void-safety: for a decade now, Eiffel has been void-safe, meaning a compile-time guarantee of no run-time null pointer dereferencing. It is beyond my understanding how the rest of the world can still live with programs that run under myriad swords of Damocles: x.op (…) calls that might any minute, without any warning or precedent, hit a null x and crash.

Then there is the guarantee of logical consistency, which is where my class invariant (Figure 1) comes in. Maybe it scared you, but in reality it is all simple concepts, intended to make sure that you know what you are doing, and rely on tools to check that you are right. When you are writing your program, you are positing all kinds, logical assumptions, large and (mostly) small, all the time. Here, for the structure triples_from [o] to make sense, it must be a list such that:

• It contains all the triples t in the triples_table such that t.source = o.
•  It contains only those triples!

You know this when you write the program; otherwise you would not be having a “triples_from” structure. Such gems of knowledge should remain an integral part of the program. Individually they may not be rocket science, but accumulated over the lifetime of a class design, a subsystem design or a system design they collect all the intelligence that makes the software possible.  Yet in the standard process they are gone the next minute! (At best, some programmers may write a comment, but that does not happen very often, and a comment has no guarantee of precision and no effect on testing or correctness.)

Anyone who takes software development seriously must record such fundamental properties. Here we need the following invariant clause:

across triples_from as tf all

across tf.item as tp all tp.item.source = tf.cursor_index end

end

(It comes in the class, as shown in Figure 1, with the label “from_list_consistent”. Such labels are important for documentation and debugging purposes. We omit them here for brevity.)

What does that mean? If we could use Unicode (more precisely, if we could type it easily with our keyboards) we would write things like “∀ x: E | P (x)”:  for all x in E, property P holds of x. We need programming-language syntax and write this as across E as x all P (x.item) end. The only subtlety is the “.item” part, which gives us generality beyond the ∀ notation: x in the across is not an individual element of E but a cursor that moves over E. The actual element at cursor position is x.item, one of the properties of that cursor. The advantage is that the cursor has more properties, for example x.cursor_index, which gives its position in E. You do not get that with the plain “ of mathematics.

If instead of ∀ you want ∃ (there exists), use some instead of all. That is pretty much all you need to know to understand all the invariant clauses of class MULTIGRAPH as given in Figure 1.

So what the above invariant clause says is: take every position tf in triples_from; its position is tf.cursor_index and its value is tf.item. triples_from is declared as ARRAYED_LIST [LIST [TRIPLE]], so tf.cursor_index is an integer representing an object o, and tf.item is a list of triples. That list should  consist of the triples having tf.cursor_index as their source. This is the very property that we are expressing in this invariant clause, where the innermost across says: for every triple tp.item in the list, the source of that triple is the cursor index (of the outside across). Simple and straightforward, I think (although such English explanations are so much more verbose than formal versions, such as the Eiffel one here, and once you get the hang of it you will not need them any more).

How can one ever include a structure such as triples_from without expressing such a property? To put the question slightly differently: am I inside the asylum looking out, or outside the asylum looking in? Any clue would be greatly appreciated.

More properties

For the tag ( “with_”) and target lists, the properties are similar:

across triples_with as tw all across tw.item as tp all tp.item.tag = tw.key end end

across triples_to as tt all across tt.item as tp all tp.item.target = tt.cursor_index end end 

We also have some properties of array bounds:

 is_root.lower = 1 and is_root.upper = object_count

triples_from.lower = 1 and triples_from.upper = object_count

triples_to.lower = 1 and triples_to.upper = object_count

where object_count is the number of objects (nodes), and for an array a (whose bounds in Eiffel are arbitrary, not necessarily 0 or 1, and set on array creation), a.lower and a.upper are the bounds. Here we number the arrays from 1.

There are, as noted, two ways to represent rootness. We must express their consistency (or risk trouble). Two clauses of the invariant do the job:

across roots as t all is_root [t.item] end

across is_root as t all (t.item = roots.has (t.cursor_index)) end

The first one says that if we go through the list “roots” we only find elements whose “is_root” value is true; the second, that if we go through the array “is_root” we find values that are true where and only where the corresponding object, given by the cursor index, is in the “roots” set. Note that the “=” in that second property is between boolean values (if in doubt, check the type instantly in the EIffelStudio IDE!), so it means “if and only if”.

Instead of these clauses, a more concise version, covering them both, is just

roots ~ domain (is_root)

with a function domain that gives the domain of a function represented by a boolean array. The ~ operator denotes object equality, redefined in many classes, and in particular in the SET classes (“roots” is a LINKED_SET) to cover equality between sets, i.e. the property of having the same elements.

The other clauses are all similarly self-explanatory. Let us just go through the most elaborate one, successors_consistent, involving three levels of across:

across successors as httpl all                   — httpl.item: hash table of list of triples

        across httpl.item as tpl all                — tpl.item: list of triples (tpl.key: key (i.e. tag) in hash table (tag)

                  across tpl.item as tp all            — tp.item: triple

                         tp.item.tag = tpl.key

and tp.item.source = httpl.cursor_index

                   end

          end

end

You can see that I struggled a bit with this one and made provisions for not having to struggle again when I would look at the code again 10 minutes, 10 days or 10 months later. I chose (possibly strange but consistent) names such as httpl for hash-table triple, and wrote comments (I do not usually need any in invariant and other contract clauses) to remind me of the type of everything. That was not strictly needed since once again the IDE gives me the types, but it does not cost much and could help.

What this says: go over “successors”; which as you remember is an ARRAY, indexed by objects, of HASH_TABLE, where each entry of such a hash table has an element of type [LIST [TRIPLE] and a key of type INTEGER, representing the tag of a number of outgoing edges from the given object. Go over each hash table httpl. Go over the associated list of triples tpl. Then for each triple tp in this list: the tag of the triple must be the key in the hash table entry (remember, the key does denote a tag); and the source of the triple must the object under consideration, which is the current iteration index in the array of the outermost iteration.

I hope I am not scaring you at this point. Although the concepts are simple, this invariant is more sophisticated than most of those we typically write. Many invariant clauses (and preconditions, and postconditions) are very simple properties, such as x > 0 or x ≠ y. The reason this one is more elaborate is not that I am trying to be fussy but that without it I would be the one scared to death. What is elaborate here is the data structure and programming technique. Not rocket science, not anything beyond programmers typically do, but elaborate. The only way to get it right is to buttress it by the appropriate logical properties. As noted, these properties are there anyway, in the back of your head, when you write the program. If you want to be more like an electrical engineer than an electrician, you have to write them down.

There is more to contracts

Invariants are not the only kind of such “contract” properties. Here for example, from the same class, is a (slightly abbreviated) part of the postcondition (output property) of the operation that tells us, through a boolean Result, if the multigraph has an edge of given components osource, t (the tag) and otarget :

Result =

(across successors [osource] [t] as tp some

not tp.item.is_inoperative and tp.item.target = otarget

end)

In words, this clause expresses the compatibility of the operation with the “successors” view: it must answer yes if and only if otarget appears in the successor set of osource for t, and the corresponding triple is not marked inoperative.

The concrete benefits

And so? What do we get out of making these logical properties explicit? Just the intellectual satisfaction of doing things right, and the methodological guidance? No! Once you have done this work, it is all downhill. Turn on the run-time assertion monitoring option (tunable separately for preconditions, postconditions, invariants etc., and on by default in development mode), and watch your tests run. If you are like almost all of us, you will have made a few mistakes, some which will seem silly when or rather if you find them in time (but there is nothing funny about a program that crashes during operation) and some more subtle. Sit back, and just watch your contracts be violated. For example if I change “<=” to “<” in the invariant property “tw.key <= max_tag”, I get the result of Figure 5. I see the call stack that I can traverse, the object run-time structure that I can explore, and all the tools of a modern debugger for an OO language. Finding and correcting the logical flaw will be a breeze.

Figure 5: An invariant violation brings up the debugger

The difference

It will not be a surprise that I did not get all the data structures and algorithms of the class MULTIGRAPH  right the first time. The Design by Contract approach (the discipline of systematically expressing, whenever you write any software element, the associated logical properties) does lead to fewer mistakes, but everyone occasionally messes up. Everyone also looks at initial results to spot and correct mistakes. So what is the difference?

Without the techniques described here, you execute your software and patiently examine the results. In the example, you might output the content of the data structures, e.g.

List of outgoing references for every object:

        1: 1-1->1|D, 1-1->2|D, 1-1->3|D, 1-2->1|D, 1-2->2|D,  1-25->8|D, 1-7->1|D, 1-7->6|D,

1-10->8|D, 1-3->1|D, 1-3->2|D, 1-6->3|D, 1-6->4|D, 1-6->5|D

        3: 3-6->3, 3-6->4, 3-6->5, 3-9->14, 3-9->15,   3-9->16, 3-1->3, 3-1->2, 3-2->3, 3-2->2,

                  3-25->8, 3-7->3, 3-7->6, 3-10->8, 3-3->3,  3-3->2    

List of outgoing references for every object:

        1: 1-1->1|D, 1-1->2|D, 1-1->3|D, 1-2->1|D, 1-2->2|D, 1-25->8|D, 1-7->1|D, 1-7->6|D,

1-10->8|D, 1-3->1|D,  1-3->2|D, 1-6->3|D, 1-6->4|D, 1-6->5|D

        3: 3-6->3, 3-6->4, 3-6->5, 3-9->14, 3-9->15,  3-9->16, 3-1->3, 3-1->2, 3-2->3, 3-2->2,

                                 3-25->8, 3-7->3, 3-7->6, 3-10->8, 3-3->3,  3-3->2

and so on for all the structures. You check the entries one by one to ascertain that they are as expected. The process nowadays has some automated support, with tools such as JUnit, but it is still essentially manual, tedious and partly haphazard: you write individual test oracles for every relevant case. (For a more automated approach to testing, taking advantage of contracts, see [1].) Like the logical properties appearing in contracts, these oracles are called “assertions” but the level of abstraction is radically different: an oracle describes the desired result of one test, where a class invariant, or routine precondition, or postcondition expresses the properties desired of all executions.

Compared to the cost of writing up such contract properties (simply a matter of formalizing what you are thinking anyway when you write the code), their effect on testing is spectacular. Particularly when you take advantage of “across” iterators. In the example, think of all the checks and crosschecks automatically happening across all the data structures, including the nested structures as in the 3-level across clause. Even with a small test suite, you immediately get, almost for free, hundreds or thousands of such consistency checks, each decreasing the likelihood that a logical flaw will survive this ruthless process.

Herein lies the key advantage. Not that you will magically stop making mistakes; but that the result of such mistakes, in the form of contract violations, directly points to logical properties, at the level of your thinking about the program. A wrong entry in an output, whether you detect it visually or through a Junit clause, is a symptom, which may be far from the cause. (Remember Dijkstra’s comment, the real point of his famous Goto paper, about the core difficulty of programming being to bridge the gap between the static program text, which is all that we control, and its effect: the myriad possible dynamic executions.) Since the cause of a bug is always a logical mistake, with a contract violation, which expresses a logical inconsistency, you are much close to that cause.

(About those logical mistakes: since a contract violation reflects a discrepancy between intent, expressed by the contract, and reality, expressed by the code, the mistake may be on either side. And yes, sometimes it is the contract that is wrong while the implementation in fact did what is informally expected. There is partial empirical knowledge [1] of how often this is the case. Even then, however, you have learned something. What good is a piece of code of which you are not able to say correctly what it is trying to do?)

The experience of Eiffel programmers reflects these observations. You catch the mistakes through contract violations; much of the time, you find and correct the problem easily. When you do get to producing actual test output (which everyone still does, of course), often it is correct.

This is what has happened to me so far in the development of the example. I had mistakes, but converging to a correct version was a straightforward process of examining violations of invariant violations and other contract elements, and fixing the underlying logical problem each time.

By the way, I believe I do have a correct version (in the sense of the second part of the Hoare quote), on the basis not of gut feeling or wishful thinking but of solid evidence. As already noted it is hard to imagine, if the code contains any inconsistencies, a test suite surviving all the checks.

Tests and proofs

Solid evidence, not perfect; hard to imagine, not impossible. Tests remain only tests; they cannot exercise all cases. The only way to achieve demonstrable correctness is to rely on mathematical proofs performed mechanically. We have this too, with the AutoProof proof system for Eiffel, developed in recent years [1]. I cannot overstate my enthusiasm for this work (look up the Web-based demo), its results (automated proof of correctness of a full-fledged data structures and algorithms library [2]) and its potential, but it is still a research effort. The dynamic approach (meaning test-based rather than proof-based) presented above is production technology, perfected over several decades and used daily for large-scale mission-critical applications. Indeed (I know you may be wondering) it scales up without difficulty:

• The approach is progressive. Unlike fully formal methods (and proofs), it does not require you to write down every single property down to the last quantifier. You can start with simple stuff like x > 0. The more you write, the more you get, but it is the opposite of an all-or-nothing approach.
• On the practical side, if you are wondering about the consequences on performance of a delivered system: there is none. Run-time contract monitoring is a compilation option, tunable for different kinds of contracts (invariants, postconditions etc.) and different parts of a system. People use it, as discussed here, for development, testing and debugging. Most of the time, when you deliver a debugged system, you turn it off.
• It is easy to teach. As a colleague once mentioned, if you can write an if-then-else you can write a precondition. Our invariants in the above example where a bit more sophisticated, but programmers do write loops (in fact, the Eiffel loop for iterating over a structure also uses across, with “loop” and instructions instead of “all” or “some” and boolean expressions). If you can write a loop over an array, you can write a property of the array’s elements.
• A big system is an accumulation of small things. In a blog article [5] I recounted how I lost a full day of producing a series of technical diagrams of increasing complexity, using one of the major Web-based collaborative development tools. A bug of the system caused all the diagrams to reproduce the first, trivial one. I managed to get through to the developers. My impression (no more than an educated guess resulting from this interaction) is that the data structures involved were far simpler than the ones used in the above discussion. One can surmise that even simple invariants would have uncovered the bug during testing rather than after deployment.
• Talking about deployment and tools used directly on the cloud: the action in software engineering today is in DevOps, a rapid develop-deploy loop scheme. This is where my perplexity becomes utter cluelessness. How can anyone even consider venturing into that kind of exciting but unforgiving development model without the fundamental conceptual tools outlined above?

We are back then to the core question. These techniques are simple, demonstrably useful, practical, validated by years of use, explained in professional books (e.g. [6]), introductory programming textbooks (e.g. [7]), EdX MOOCs (e.g. [8]), YouTube videos, online tutorials at eiffel.org, and hundreds of articles cited thousands of times. On the other hand, most people reading this article are not using Eiffel. On reflection, a simple quantitative criterion does exist to identify the inmates: there are far more people outside the asylum than inside. So the evidence is incontrovertible.

What, then, is wrong with me?

References

(Nurse to psychiatrist: these are largely self-references. Add “narcissism” to list of patient’s symptoms.)

1.    Ilinca Ciupa, Andreas Leitner, Bertrand Meyer, Manuel Oriol, Yu Pei, Yi Wei and others: AutoTest articles and other material on the AutoTest page.

2. Bertrand Meyer, Ilinca Ciupa, Lisa (Ling) Liu, Manuel Oriol, Andreas Leitner and Raluca Borca-Muresan: Systematic evaluation of test failure results, in Workshop on Reliability Analysis of System Failure Data (RAF 2007), Cambridge (UK), 1-2 March 2007 available here.

3.    Nadia Polikarpova, Ilinca Ciupa and Bertrand Meyer: A Comparative Study of Programmer-Written and Automatically Inferred Contracts, in ISSTA 2009: International Symposium on Software Testing and Analysis, Chicago, July 2009, available here.

4.    Carlo Furia, Bertrand Meyer, Nadia Polikarpova, Julian Tschannen and others: AutoProof articles and other material on the AutoProof page. See also interactive web-based online tutorial here.

5.    Bertrand Meyer, The Cloud and Its Risks, blog article, October 2010, available here.

6.    Bertrand Meyer: Object-Oriented Software Construction, 2^nd edition, Prentice Hall, 1997.

7.    Bertrand Meyer: Touch of Class: Learning to Program Well Using Objects and Contracts, Springer, 2009, see touch.ethz.ch and Amazon page.

8.    MOOCs (online courses) on EdX : Computer: Art, Magic, Science, Part 1 and Part 2. (Go to “archived versions” to follow the courses.)

Every couple of weeks or so, I receive a message such as the one below; whenever I give a talk on any computer science topic anywhere in the world, strangers come to me to express similar sentiments. While I enjoy compliments as much as anyone else, I am not the right recipient for such comments. In fact there are 7,599,999,999  more qualified recipients. For me, Eiffel is “mainstream” enough.

What strikes me is why so many commenters, after the compliment, stop at the lament. Eiffel is not some magical dream, it is a concrete technology available for download at eiffel.org. Praising Eiffel will not change the world. Using EiffelStudio might.

When one answers the compliments with “Thanks! Then use it for your work“, the variety of excuses is amusing, or sad depending on the perspective, from “my boss would not allow it” (variant: “my subordinates would not accept it”) to “does it work with [library that does not work with anything else]?”.

Well, you might have some library wrapping to do (EiffelStudio easily interfaces with C, C++ and others). Also, you should not stop at the first hurdle: it might be due to a bug (surprise! The technology is not perfect!), but it might also just be that Eiffel and EiffelStudio are different and you have to shed some long-held assumptions and practices. What matters is that the technology does work; companies large and small use Eiffel all the time for long-running projects, some into the millions of lines and tens of thousands of classes, and refuse to switch to anything else.

What follows is a literal translation of the original message into English (it was written in another language). Since the author, whom I do not know, did not state the email was a public comment, I removed identifying details.

Subject:Eiffel is fantastic! But why is it not mainstream?

Dear Professor Meyer:

Greetings from [the capital of a country on another continent].

I graduated from [top European university] in 1996 and completed a master’s in physics from [institute on another continent] in 2006.

I have worked for twenty years in the industry, from application engineer to company head. In my industry career I have been able to be both CEO and CTO at the same time, thanks to the good education I received originally.

Information systems were always a pillar of my business strategy. Unfortunately, I was disappointed every single time I commissioned the development of a new system. This led me to study further and to investigate why the problem is not solved. That’s how I found your book Object-Oriented Software Construction and became enthusiastic about Design by Contract, Eiffel and EiffelStudio. To me your method is the only method for developing “correct” software. The Eiffel programming language is, in my view, the only true object-oriented language.

However it befuddles me — I cannot understand —  why the “big” players in this industry (Apple, Google, Microsoft etc.) do not use Design by Contract. .NET has a Visual Studio extension with the name “Code Contracts” but it is no longer supported in the latest Visual Studio 2017. Big players, why don’t you promote Design by Contract?

Personally, after 20 years in industry, I found out that my true calling is in research. It would be a great pleasure to be able to work in research. My dream job is Data Scientist and I had thought to apply to Google for a job. Studying the job description, I noted that “Python” is one of the desired languages. Python is dynamically typed and does not support good encapsulation. No trace of Design by Contract…

What’s wrong with the software industry?

With best regards,

(Adapted from a two-part article on the Communications of the ACM blog.)

1 The rise of empirical software engineering

One of the success stories of software engineering research in recent decades has been the rise of empirical studies. Visionaries such as Vic Basili, Marvin Zelkowitz and Walter Tichy advocated empirical techniques early [1, 2, 3]; what enabled the field to take off was the availability of software repositories for such long-running projects as Apache, Linux and Eclipse [4], which researchers started mining using modern data analysis techniques.

These studies have yielded many insights including surprises. More experienced developers can produce more buggy code (Schröter, Zimmermann, Premraj, Zeller). To predict whether a module has bugs, intrinsic properties such as complexity seem to matter less than how many changes it went through (Moser, Pedrycz, Succi). Automatic analysis of user reports seems much better at identifying bugs than spotting feature requests (Panichella, Di Sorbo, Guzman, Visaggio, Canfora, Gall). More extensively tested modules tend to have more bugs (Mockus, Nagappan, Dinh-Trong). Eiffel programmers do use contracts (Estler, Furia, Nordio, Piccioni and me). Geographical distance between team members negatively affects the amount of communication in projects (Nordio, Estler, Tschannen, Ghezzi, Di Nitto and me). And so on.

The basic observation behind empirical software engineering is simple: if software products and processes are worthy of discussion, they must be worthy of quantitative discussion just like any natural artifact or human process. Usually at that point the advocacy cites Lord Kelvin:”If you cannot measure it, you cannot improve it” [5].

Not that advocacy is much needed today, at least for publishing research in software engineering and in computer science education. The need for empirical backing of conceptual proposals has achieved consensus.  The so-called a “Marco Polo paper” [6] (I traveled far and saw wonderful things, thank you very much for your attention) no longer suffices for program committees; today they want numbers (and also, thankfully, a “threats to validity” section which protects you against suspicions that the numbers are bogus by stating why they might be). Some think this practice of demanding empirical backing for anything you propose has gone too far; see Jeff Ullman’s complaint [7], pertaining to database research rather than software engineering, but reflecting some of the same discussions. Here we can counter Kelvin with another quote (for more effect attributed to Einstein, albeit falsely): not everything that can be counted counts, and not everything that counts can be counted.

2 Limits of empirical research

There can indeed be too much of a good thing. Still, no one would seriously deny the fundamental role that empirical research has gained in modern software engineering. Which does not prevent us from considering the limits of what it has achieved; not in a spirit of criticism for its own sake, but to help researchers define an effective agenda for the next steps. There are in my opinion two principal limitations of current empirical results in software engineering.

The first has to do with the distinction introduced above between the two kinds of possible targets for empirical assessment: products (artifacts) versus processes.

Both aspects are important, but one is much easier to investigate than the other. For software products, the material of study is available in the form of repositories mentioned above, with their wealth of information about lines of code, control and data structures, commits, editing changes, bug reports and bug fixes. Processes are harder to grasp. You gain some information on processes from the repositories (for example, patterns and delays of bug fixing), but processes deserve studies of their own. For example, agile teams practice iterations (sprints) of widely different durations, from a few days to a few weeks; what is the ideal length? A good empirical answer would help many practitioners. But this example illustrates how difficult empirical studies of processes can be: you would need to try many variations with teams of professional programmers (not students) in different projects, different application areas, different companies; for the results to be believable the projects should be real ones with business results at stake, there should be enough samples in each category to ensure statistical significance, and the companies should agree to publication of some form, possibly anonymized, of the outcomes. The difficulties are formidable.

This issue of how to obtain project-oriented metrics is related to the second principal limitation of some of the initial empirical software engineering work: the risk of indulging in lamppost research. The term refers to the well-known joke about the drunkard who, in the dark of the night, searches for his lost keys next to the lamp post, not because he has lost them there but because it is the only place where one can see anything. To a certain extent all research is lamppost research: by definition, if you succeed in studying something, it will be because it can be studied. But the risk is to choose to work on a problem only, or principally, because it is easy to set up an empirical study — regardless of its actual importance. To cite an example that I have used elsewhere, one may suspect that the reason there are so many studies of pair programming is not that it’s of momentous relevance but that it is not hard to set up an experiment.

3 Beyond the lamppost

As long as empirical software engineering was a young, fledgling discipline, it made good sense to start with problems that naturally lended themselves to empirical investigation. But now that the field has matured, it may be time to reverse the perspective and start from the consumer’s perspective: for practitioners of software engineering, what problems, not yet satisfactorily answered by software engineering theory, could benefit, in the search for answers, from empirical studies?

Indeed, this is what we are entitled to expect from empirical studies: guidance. The slogan of empirical software engineering is that software is worthy of study just like geological strata, photons, and lilies-of-the-valley; OK, sure, but we are talking about human artifacts rather than wonders of the natural world, and the idea should be to help us produce better software and produce software better.

4 A horror story

Whenever we call for guidance from empirical studies, we should immediately include a caveat: every empirical study has its limitations (politely called “threats to validity”) and one must be careful about any generalization. The following horror story serves as caution [9]. The fashion today in programming language design is to use the semicolon not as separator in the Algol tradition (instruction1 ; instruction2) but as a terminator in the C tradition (instruction1; instruction2;). The original justification, particularly in the case of Ada [10], is an empirical paper by Gannon and Horning [11], which purported to show that the terminator convention led to fewer errors. (The authors themselves not only give their experimental results but, departing from the experimenter’s reserve, explicitly jump to the conclusion that terminators are better.) This view defies reason: witness, among others, the ever-recommenced tragedy of if c then a; else; b where the semicolon after else is an error (a natural one, since one gets into the habit of adding semicolons just in case) but the code compiles, with the result that b will be executed in all cases rather than (as intended) just when c is false [12].

How in the world could an empirical study come up with such a bizarre conclusion? Go back to the original Gannon-Horning paper and the explanation becomes clear: the experiments used subjects who were familiar with the PL/I programming language, where semicolons are used generously and an extra semicolon is harmless, as it is in all practical languages (two successive semicolons being simply interpreted as the insertion of an empty instruction, causing no harm); but the experimental separator-based language and compiler used to the experiment treated an extra semicolon as an error! As if this were not enough, checking the details of the article reveals that the terminator language is terminator-based for both declarations and instructions, whereas the example delimiter language is only delimiter-based for instructions, but terminator-based for declarations. Talk about a biased experiment! The experiment was bogus and so are the results.

One should not be too harsh about a paper from 1975, when the very idea of systematic experimental studies of programming was novel, and some of its other results are worthy of consideration. But the sad terminator story, even though it only affected a syntax property, should serve as a reminder that we should not accept a view blindly just because someone invokes some empirical study to justify it. We should assess the study itself, its methods and its credibility.

5 Addressing the issues that matter

With this warning in mind, we should still expect empirical software engineering to help us practitioners. It should help address important software engineering problems.

Ideally, I should now list the open issues of software engineering, but I am in no position even to start such a list. All I can do is to give a few examples. They may not be important to you, but they give an idea:

• What are the respective values of upfront design and refactoring? How best can we combine these approaches?
• Specification and testing are complementary techniques. Specifications are in principles superior to testing in general, but testing remains necessary. What combination of specification and testing works best?
• What is the best commit/release technique, and in particular should we use RTC (Review Then Commit, as with Apache originally then Google) or CTR (Commit To Review, as Apache later) [13]?
• What measure of code properties best correlates with effort? Many fancy metrics have appeared in the literature over the years, but there is still a nagging feeling among many of us that for all its obvious limitations the vulgar SLOC metrics (Source Lines Of Code) still remains the least bad.
• When can a manager decide to stop testing? We did some work on the topic [14], but it is only a start.
• Is test coverage a good measure of test quality [15] (spoiler: it is not, but again we need more studies)?

And so on. These examples may not be the cases that you consider most important; indeed what we need is input from many software engineers to help steer empirical software engineering towards the topics that truly matter to the community.

To provide a venue for that discussion, a workshop will take place 10-12 September 2018 (provisional dates) in the Toulouse area, involving many of the tenors in empirical software engineering, with the same title as these two articles: Empirical Answers to Important Software Engineering Questions. The key idea is to start not from the solutions side (the lamppost) but from the actual challenges facing software engineers. It will not just be a traditional publication-oriented meeting but will also include ample time for discussions and joint work.

If you would like to contribute your example “important questions”, please use any appropriate support (responses to this blog, email to me, Facebook, LinkedIn, anything as long as one can find it). Suggestions will be taken into consideration for the workshop. Empirical software engineering has already established itself as a core area of research; it is time feed that research with problems that actually matter to software developers, managers and users

Acknowledgments

These reflections originated in a keynote that I gave at ESEM in Bolzano in 2010 (I am grateful to Barbara Russo and Giancarlo Succi for the invitation). I never wrote up the talk but I dug up the slides [8] since they might contain a few relevant observations. I used some of these ideas in a short panel statement at ESEC/FSE 2013 in Saint Petersburg, and I am grateful to Moshe Vardi for suggesting I should write them up for Communications of the ACM, which I never did.

References and notes

[1] Victor R. Basili: The role of experimentation in software engineering: past, present and future,  in 18th ICSE (International Conference on Software Engineering), 1996, see here.

[2] Marvin V. Zelkowitz and Dolores Wallace: Experimental validation in software engineering, International Conference on Empirical Assessment and Evaluation in Software Engineering, March 1997, see here.

[3] Walter F. Tichy: Should computer scientists experiment more?, in IEEE Computer, vol. 31, no. 5, pages 32-40, May 1998, see here.

[4] And EiffelStudio, whose repository goes back to the early 90s and has provided a fertile ground for numerous empirical studies, some of which appear in my publication list.

[5] This compact sentence is how the Kelvin statement is usually abridged, but his thinking was more subtle.

[6] Raymond Lister: After the Gold Rush: Toward Sustainable Scholarship in Computing, Proceedings of 10th conference on Australasian Computing Education Conference, pages 3-17, see here.

[7] Jeffrey D. Ullman: Experiments as research validation: have we gone too far?, in Communications of the ACM, vol. 58, no. 9, pages 37-39, 2015, see here.

[8] Bertrand Meyer, slides of a talk at ESEM (Empirical Software Engineering and Measurement), Bozen/Bolzano, 2010, available here. (Provided as background material only, they are  not a paper but just slide support for a 45-minute talk, and from several years ago.)

[9] This matter is analyzed in more detail in section 26.5 of my book Object-Oriented Software Construction, 2nd edition, Prentice Hall. No offense to the memory of Jim Horning, a great computer scientist and a great colleague. Even great computer scientists can be wrong once in a while.

[10] I know this from the source: Jean Ichbiah, the original designer of Ada, told me explicitly that this was the reason for his choice of  the terminator convention for semicolons, a significant decision since it was expected that the language syntax would be based on Pascal, a delimiter language.

[11] Gannon & Horning, Language Design for Programming Reliability, IEEE Transactions on Software Engineering, vol. SE-1, no. 2, June 1975, pages 179-191, see here.

[12] This quirk of C and similar languages is not unlike the source of the Apple SSL/TLS bug discussed earlier in this blog under the title Code matters.

[13] Peter C. Rigby, Daniel M. German, Margaret-Anne Storey: Open Source Software Peer Review Practices: a Case study of the Apache Server, in ICSE (International Conference on Software Engineering) 2008, pages 541-550, see here.

[14] Carlo A. Furia, Bertrand Meyer, Manuel Oriol, Andrey Tikhomirov and  Yi Wei:The Search for the Laws of Automatic Random Testing, in Proceedings of the 28th ACM Symposium on Applied Computing (SAC 2013), Coimbra (Portugal), ACM Press, 2013, see here.

[15] Yi Wei, Bertrand Meyer and Manuel Oriol: Is Coverage a Good Measure of Testing Effectiveness?, in Empirical Software Engineering and Verification (LASER 2008-2010), eds. Bertrand Meyer and Martin Nordio, Lecture Notes in Computer Science 7007, Springer, February 2012, see here.

Many programs take “execution arguments” which the program users provide at the start of execution. In EiffelStudio you can enter them under Execution -> Execution parameters.

The program can access them through the Kernel Library class ARGUMENTS. Typically, the root class of the system inherits from ARGUMENTS and its creation procedure will include something like

if argument_count /= N then
……..print (“XX expects exactly N arguments: AA, BB, …%N”)
else
……..u := argument (1) ; v := argument (2) ; …
……..“Proceed with normal execution, using u, v, …”
end

where N is the number of expected arguments, XX is the name of the program, and AA, …. are the roles of arguments. u, v, … are local variables. The criterion for acceptance could be “at least N” instead of exactly N. The features argument_count and arguments come from class ARGUMENTS.

In all but trivial cases this scheme (which was OK years ago, in a less sophisticated state of the language) does not work! The reason is that the error branch will fail to initialize attributes. Typically, the “Proceed with…” part in the other branch is of the form

               attr1 := u
                attr2 := v
                …
                create obj1.make (attr1, …)
                create obj2.make (attr2, …)
                “Work with obj1, obj2, …”

If you try to compile code of this kind, you will get a compilation error:

Eiffel is void-safe: it guarantees that no execution will ever produce null-pointer dereference (void call). To achieve this guarantee, the compiler must make sure that all attributes are “properly set” to an object reference (non-void) at the end of the creation procedure. But the error branch fails to initialize obj1 etc.

You might think of replacing the explicit test by a precondition to the creation procedure:

               require
                                argument_count = N

but that does not work; the language definition explicit prohibits preconditions in a root creation procedure. The Ecma-ISO standard (the official definition of the language, available here) explains the reason for the corresponding validity rule (VSRP, page 32):

A routine can impose preconditions on its callers if these callers are other routines; but it makes no sense to impose a precondition on the external agent (person, hardware device, other program…) that triggers an entire system execution, since there is no way to ascertain that such an agent, beyond the system’s control, will observe the precondition.

The solution is to separate the processing of arguments from the rest of the program’s work. Add a class CORE which represents the real core of the application and separate it from the root class, say APPLICATION. In APPLICATION, all the creation procedure does is to check the arguments and, if they are fine, pass them on to an instance of the core class:

                note
                                description: “Root class, processes execution arguments and starts execution”
                class APPLICATION create make feature
                                core: CORE
                                                — Application’s core object
                                make
……..……..……..……..……..……..— Check arguments and proceed if they make sense.
                                                do
                                                             if argument_count /= N then
                                                                                print (“XX expects exactly N arguments: AA, BB, …%N”)
                                                                else
                                                                                create core.make (argument (1), argument (2) ; …)
                                                                                                — By construction the arguments are defined!
                                                                                core.live
                                                                                                — Perform actual work
                                                                                               — (`live’ can instead be integrated with `make’ in CORE.)

                                                                end
                                                end
                 end
 
We may call this little design pattern “Split the Root”. Nothing earth-shattering; it is simply a matter of separating concerns (cutting off the Model from the View). It assumes a system that includes text-based output, whereas many applications are graphical. It is still worth documenting, for two reasons.

First, in its own modest way, the pattern is useful for simple programs; beginners, in particular, may not immediately understand why the seemingly natural way of processing and checking arguments gets rejected by the compiler.

The second reason is that Split the Root illustrates the rules that preside over a carefully designed language meant for carefully designed software. At first it may be surprising and even irritating to see code rejected because, in a first attempt, the system’s root procedure has a precondition, and in a second attempt because some attributes are not initialized — in the branch where they do not need to be initialized. But there is a reason for these rules, and once you understand them you end up writing more solid software.

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

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

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

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

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

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

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

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

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

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

References

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

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.

In support of his view of software methodology, Leslie Lamport likes to use the example of non-recursive Quicksort. Independently of the methodological arguments, his version of the algorithm should be better known. In fact, if I were teaching “data structures and algorithms” I would consider introducing it first.

As far as I know he has not written down his version in an article, but he has presented it in lectures; see [1]. His trick is to ask the audience to give a non-recursive version of Quicksort, and of course everyone starts trying to remove the recursion, for example by making the stack explicit or looking for invertible functions in calls. But his point is that recursion is not at all fundamental in Quicksort. The recursive version is a specific implementation of a more general idea.

Lamport’s version — let us call it Lampsort —is easy to express in Eiffel. We may assume the following context:

a: ARRAY [G -> COMPARABLE]        — The array to be sorted.
pivot: INTEGER                                      —  Set by partition.
picked: INTEGER_INTERVAL            — Used by the sorting algorithm, see below.
partition (i, j: INTEGER)
……..require      — i..j is a sub-interval of the array’s legal indexes:
……..……..i < j
……..……..i >= a.lower
……..……..j <= a.upper
……..do
……..……..… Usual implementation of partition …
……..ensure     — The expected effect of partition:
……..……..pivot >= i
……..……..pivot < j
……..……..— a [i..j] has been reshuffled so that elements in i..pivot are less than
……..……..— or equal to those in pivot+1 .. j.
……..end

We do not write the implementation of partition since the point of the present discussion is the overall algorithm. In the usual understanding, that algorithm consists of doing nothing if the array has no more than one element, otherwise performing a partition and then recursively calling itself on the two resulting intervals. The implementation can take advantage of parallelism by forking the recursive calls out to different processors. That presentation, says Lamport, describes only a possible implementation. The true Quicksort is more general. The algorithm works on a set not_sorted of integer intervals i..j such that the corresponding array slices a [i..j] are the only ones possibly not sorted; the goal of the algorithm is to make not_sorted empty, since then we know the entire array is sorted. In Eiffel we declare this set as:

not_sorted: SET [INTEGER_INTERVAL]

The algorithm initializes not_sorted to contain a single element, the entire interval; at each iteration, it removes an interval from the set, partitions it if that makes sense (i.e. the interval has more than one element), and inserts the resulting two intervals into the set. It ends when not_sorted is empty. Here it is:

……..from                                 — Initialize interval set to contain a single interval, the array’s entire index range:
……..…..create not_sorted.make_one (a.lower |..| a.upper)….         ..……..
……..invariant
……..…..— See below
……..until
……..…..not_sorted.is_empty                                                            — Stop when there are no more intervals in set
……..loop
……..…..picked := not_sorted.item                                                     — Pick an interval from (non-empty) interval set.
……..……if picked.count > 1 then                                                      — (The precondition of partition holds, see below.)
……..……..…..partition (picked.lower, picked.upper)                 — Split, moving small items before & large ones after pivot.
……..……..…..not_sorted.extend (picked.lower |..| pivot)            — Insert new intervals into the set of intervals: first
……..……....…not_sorted.extend (pivot + 1 |..| picked.upper)     — and second.
……..……end
……..…...not_sorted.remove (picked)                                               — Remove interval that was just partitioned.
…….end

Eiffel note: the function yielding an integer interval is declared in the library class INTEGER using the operator |..| (rather than just  ..).

The query item from SET, with the precondition not is_empty,  returns an element of the set. It does not matter which element. In accordance with the Command-Query Separation principle, calling item does not modify the set; to remove the element you have to use the command remove. The command extend adds an element to the set.

The abstract idea behind Lampsort, explaining why it works at all, is the following loop invariant (see [2] for a more general discussion of how invariants provide the basis for understanding loop algorithms). We call “slice” of an array a non-empty contiguous sub-array; for adjacent slices we may talk of concatenation; also, for slices s and t,  s <= t means that every element of s is less than or equal to every element of t. The invariant is:

a is the concatenation of the members of a set slices of disjoint slices, such that:
– The elements of a are a permutation of its original elements.
– The index range of any member  of slices having more than one element is in not_sorted.
– For any adjacent slices s and t (with s before t), s <= t.

The first condition (conservation of the elements modulo permutation) is a property of partition, the only operation that can modify the array. The rest of the invariant is true after initialization (from clause) with slices made of a single slice, the full array. The loop body maintains it since it either removes a one-element interval from not_sorted (slices loses the corresponding slice) or performs partition with the effect of partitioning one slice into two adjacent ones satisfying s <= t, whose intervals replace the original one in not_sorted. On exit, not_sorted is empty, so slices is a set of one-element slices, each less than or equal to the next, ensuring that the array is sorted.

The invariant also ensures that the call to partition satisfies that routine’s precondition.

The Lampsort algorithm is a simple loop; it does not use recursion, but relies on an interesting data structure, a set of intervals. It is not significantly longer or more difficult to understand than the traditional recursive version

sort (i, j: INTEGER)
……..require
……..……..i <= j
……..……..i >= a.lower
……..……..j <= a.upper
……..do
……..……if j > i then                    — Note that precondition of partition holds.
……..……..…..partition (i, j)         — Split into two slices s and t such that s <= t.
……..……..…..sort (i, pivot)          — Recursively sort first slice.
……..……..…..sort (pivot+1, j)      — Recursively sort second slice.
……..……end……..…..
……..end

Lampsort, in its author’s view, captures the true idea of Quicksort; the recursive version, and its parallelized variants, are only examples of possible implementations.

I wrote at the start that the focus of this article is Lampsort as an algorithm, not issues of methodology. Let me, however, give an idea of the underlying methodological debate. Lamport uses this example to emphasize the difference between algorithms and programs, and to criticize the undue attention being devoted to programming languages. He presents Lampsort in a notation which he considers to be at a higher level than programming languages, and it is for him an algorithm rather than a program. Programs will be specific implementations guided in particular by efficiency considerations. One can derive them from higher-level versions (algorithms) through refinement. A refinement process may in particular remove or restrict non-determinism, present in the above version of Lampsort through the query item (whose only official property is that it returns an element of the set).

The worldview underlying the Eiffel method is almost the reverse: treating the whole process of software development as a continuum; unifying the concepts behind activities such as requirements, specification, design, implementation, verification, maintenance and evolution; and working to resolve the remaining differences, rather than magnifying them. Anyone who has worked in both specification and programming knows how similar the issues are. Formal specification languages look remarkably like programming languages; to be usable for significant applications they must meet the same challenges: defining a coherent type system, supporting abstraction, providing good syntax (clear to human readers and parsable by tools), specifying the semantics, offering modular structures, allowing evolution while ensuring compatibility. The same kinds of ideas, such as an object-oriented structure, help on both sides. Eiffel as a language is the notation that attempts to support this seamless, continuous process, providing tools to express both abstract specifications and detailed implementations. One of the principal arguments for this approach is that it supports change and reuse. If everything could be fixed from the start, maybe it could be acceptable to switch notations between specification and implementation. But in practice specifications change and programs change, and a seamless process relying on a single notation makes it possible to go back and forth between levels of abstraction without having to perform repeated translations between levels. (This problem of change is, in my experience, the biggest obstacle to refinement-based approaches. I have never seen a convincing description of how one can accommodate specification changes in such a framework without repeating the whole process. Inheritance, by the way, addresses this matter much better.)

The example of Lampsort in Eiffel suggests that a good language, equipped with the right abstraction mechanisms, can be effective at describing not only final implementations but also abstract algorithms. It does not hurt, of course, that these abstract descriptions can also be executable, at the possible price of non-optimal performance. The transformation to an optimal version can happen entirely within the same method and language.

Quite apart from these discussions of software engineering methodology, Lamport’s elegant version of Quicksort deserves to be known widely.

References

[1] Lamport video here, segment starting at 0:32:34.
[2] Carlo Furia, Bertrand Meyer and Sergey Velder: Loop invariants: Analysis, Classification and Examples, in ACM Computing Surveys, September 2014, preliminary text here.

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

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

References

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

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

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.

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

Here is the abstract:

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

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

Reference

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

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

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

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

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

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

model = <x> + old model         /B/

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

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

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

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

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

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

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

References

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

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

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

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

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

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

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

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.

Lack of a precise context can render discussions of software engineering and particularly of software quality meaningless. Take for example the (usually absurd) statement “We cannot expect that programmers will equip their programs with contracts”. Whom do you mean? A physicist who writes 50 lines of Matlab code to produce a graph illustrating his latest experiment? A member of the maintenance team for Microsoft Word? A programmer on the team for a flight control system? These are completely different constituencies, and the answer is also different. In the last case, the answer is probably that we do not care what the programmers like and do not like. When you buy an electrical device that malfunctions, would you accept from the manufacturer the excuse that differential equations are, really, you see, too hard for our electrical engineers?

In discussing the evolution of software methods and tools we must first specify what and whom we are talking about. The following ABC characterization is sufficient for most cases.

C is for Casual. Programs in that category do all kinds of useful things, and like anything else they should work properly, but if they are not ideal in software engineering terms of reliability, reusability, extendibility and so on — if sometimes they crash, sometimes produce not-quite-right results,  cannot be easily understood or maintained by anyone other than their original developers, target just one platform, run too slowly, eat up too much memory, are not easy to change, include duplicated code — it is not the end of the world. I do not have any scientific figures, but I suspect that most of the world’s software is actually in that category, from JavaScript or Python code that runs web sites to spreadsheet macros. Obviously it has to be good enough to serve its needs, but “good enough” is good enough.

B is for Business. Programs in that category run key processes in the organization. While often far from impeccable, they must satisfy strict quality constraints; if they do not, the organization will suffer significantly.

A is for Acute. This is life-critical software: if it does not work — more precisely, if it does not work exactly right — someone will get killed, someone will lose huge amounts of money, or something else will go terribly wrong. We are talking transportation systems, software embedded in critical devices, make-or-break processes of an organization.

Even in a professional setting, and even within a single company, the three categories usually coexist. Take for example a large engineering or scientific organization.  Some programs are developed to support experiments or provide an answer to a specific technical question. Some programs run the organization, both on the information systems side (enterprise management) and on the technical side (large scientific simulations, experiment set-up). And some programs play a critical role in making strategy decisions, or run the organization’s products.

The ABC classification is independent of the traditional division between enterprise and technical computing. Organizations often handle these two categories separately, whereas in fact they raise issues of similar difficulty and are subject to solutions of a similar nature. It is more important to assess the criticality of each software projects, along the ABC scale.

It is surprising that few organizations make that scale explicit.  It is partly a consequence of that neglect that many software quality initiatives and company-wide software engineering policies are ineffective: they lump everything together, and since they tend to be driven by A-grade applications, for which the risk of bad quality is highest, they create a burden that can be too high for C- and even B-grade developments. People resent the constraints where they are not justified, and as a consequence ignore them where they would be critical. Whether your goal for the most demanding projects is to achieve CMMI qualification or to establish an effective agile process, you cannot impose the same rules on everyone. Sometimes the stakes are high; and sometimes a program is just a program.

The first step in establishing a successful software policy is to separate levels of criticality, and require every development to position itself along the resulting scale. The same observation qualifies just about any discussion of software methodology. Acute, Business or Casual: you must know your ABC.

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

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

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

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

References

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

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

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

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

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.