Posts tagged ‘Hoare’

The story of our field, in a few short words

 

(With all dues to [1], but going up from four to five as it is good to be brief yet not curt.)

At the start there was Alan. He was the best of all: built the right math model (years ahead of the real thing in any shape, color or form); was able to prove that no one among us can know for sure if his or her loops — or their code as a whole — will ever stop; got to crack the Nazis’ codes; and in so doing kind of saved the world. Once the war was over he got to build his own CPUs, among the very first two or three of any sort. But after the Brits had used him, they hated him, let him down, broke him (for the sole crime that he was too gay for the time or at least for their taste), and soon he died.

There was Ed. Once upon a time he was Dutch, but one day he got on a plane and — voilà! — the next day he was a Texan. Yet he never got the twang. The first topic that had put him on  the map was the graph (how to find a path, as short as can be, from a start to a sink); he also wrote an Algol tool (the first I think to deal with all of Algol 60), and built an OS made of many a layer, which he named THE in honor of his alma mater [2]. He soon got known for his harsh views, spoke of the GOTO and its users in terms akin to libel, and wrote words, not at all kind, about BASIC and PL/I. All this he aired in the form of his famed “EWD”s, notes that he would xerox and send by post along the globe (there was no Web, no Net and no Email back then) to pals and foes alike. He could be kind, but often he stung. In work whose value will last more, he said that all we must care about is to prove our stuff right; or (to be more close to his own words) to build it so that it is sure to be right, and keep it so from start to end, the proof and the code going hand in hand. One of the keys, for him, was to use as a basis for ifs and loops the idea of a “guard”, which does imply that the very same code can in one case print a value A and in some other case print a value B, under the watch of an angel or a demon; but he said this does not have to be a cause for worry.

At about that time there was Wirth, whom some call Nick, and Hoare, whom all call Tony. (“Tony” is short for a list of no less than three long first names, which makes for a good quiz at a party of nerds — can you cite them all from rote?) Nick had a nice coda to Algol, which he named “W”; what came after Algol W was also much noted, but the onset of Unix and hence of C cast some shade over its later life. Tony too did much to help the field grow. Early on, he had shown a good way to sort an array real quick. Later he wrote that for every type of unit there must be an axiom or a rule, which gives it an exact sense and lets you know for sure what will hold after every run of your code. His fame also comes from work (based in part on Ed’s idea of the guard, noted above) on the topic of more than one run at once, a field that is very hot today as the law of Moore nears its end and every maker of chips has moved to  a mode where each wafer holds more than one — and often many — cores.

Dave (from the US, but then at work under the clime of the North) must not be left out of this list. In a paper pair, both from the same year and both much cited ever since,  he told the world that what we say about a piece of code must only be a part, often a very small part, of what we could say if we cared about every trait and every quirk. In other words, we must draw a clear line: on one side, what the rest of the code must know of that one piece; on the other, what it may avoid to know of it, and even not care about. Dave also spent much time to argue that our specs must not rely so much on logic, and more on a form of table.  In a later paper, short and sweet, he told us that it may not be so bad that you do not apply full rigor when you chart your road to code, as long as you can “fake” such rigor (his own word) after the fact.

Of UML, MDA and other such TLAs, the less be said, the more happy we all fare.

A big step came from the cold: not just one Norse but two, Ole-J (Dahl) and Kris, came up with the idea of the class; not just that, but all that makes the basis of what today we call “O-O”. For a long time few would heed their view, but then came Alan (Kay), Adele and their gang at PARC, who tied it all to the mouse and icons and menus and all the other cool stuff that makes up a good GUI. It still took a while, and a lot of hit and miss, but in the end O-O came to rule the world.

As to the math basis, it came in part from MIT — think Barb and John — and the idea, known as the ADT (not all TLAs are bad!), that a data type must be known at a high level, not from the nuts and bolts.

There also is a guy with a long first name (he hates it when they call him Bert) but a short last name. I feel a great urge to tell you all that he did, all that he does and all that he will do, but much of it uses long words that would seem hard to fit here; and he is, in any case, far too shy.

It is not all about code and we must not fail to note Barry (Boehm), Watts, Vic and all those to whom we owe that the human side (dear to Tom and Tim) also came to light. Barry has a great model that lets you find out, while it is not yet too late, how much your tasks will cost; its name fails me right now, but I think it is all in upper case.  At some point the agile guys — Kent (Beck) and so on — came in and said we had got it all wrong: we must work in pairs, set our goals to no more than a week away, stand up for a while at the start of each day (a feat known by the cool name of Scrum), and dump specs in favor of tests. Some of this, to be fair, is very much like what comes out of the less noble part of the male of the cow; but in truth not all of it is bad, and we must not yield to the urge to throw away the baby along with the water of the bath.

I could go on (and on, and on); who knows, I might even come back at some point and add to this. On the other hand I take it that by now you got the idea, and even on this last day of the week I have other work to do, so ciao.

Notes

[1] Al’s Famed Model Of the World, In Words Of Four Signs Or Fewer (not quite the exact title, but very close): find it on line here.

[2] If not quite his alma mater in the exact sense of the term, at least the place where he had a post at the time. (If we can trust this entry, his true alma mater would have been Leyde, but he did not stay long.)

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Specifying user interfaces

Many blogs including this one rely on the WordPress software. In previous states of the present page you may have noticed a small WordPress bug, which I find interesting.

“Tags” are a nifty WordPress feature. When you post a message, you can specify one or more informative “tags”. The tags of all messages appear in the right sidebar, each with a smaller or bigger font size depending on the number of messages that specified it. You can click such a tag in the sidebar and get, on the left, a page containing all the associated messages.

Now assume that many posts use a particular tag; in our example it is “Design by Contract”, not unexpected for this blog. Assume further that the tag name is long. It is indeed in this case: 18 characters. As a side note, no problem would arise if I used normal spaces in the name, which would then appear on two or three lines; precisely to avoid this  I use HTML “non-breaking spaces”. This is probably not in the WordPress spirit, but any other long tag without spaces would create the same problem. That problem is a garbled display:

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The long tag overflows the bluish browser area assigned to tags, producing an ugly effect. This behavior is hard to defend: either the tag should have been rejected as too long when the poster specified it or it should fit in its zone, whether by truncation or by applying a smaller font.

I quickly found a workaround, not nice but good enough: make sure that some short tag  (such as “Hoare”) appears much more often than the trouble-making tag. Since font size indicates the relative frequency of tags, the long one will be scaled down to a smaller font which fits.

Minor as it is, this WordPress glitch raises some general questions. First, is it really a bug? Assume, by a wild stretch of imagination, that a jury had to resolve this question; it could easily find an expert to answer positively, by stating that the behavior does not satisfy reasonable user expectations, and another who notes that it is not buggy behavior since it does not appear to violate any expressly stated property of the specification. (At least I did not find in the WordPress documentation any mention of either the display size of tags or a limit on tag length; if I missed it please indicate the reference.)

Is it a serious matter? Not in this particular example; uncomely Web display does not kill.   But the distinction between “small matter of esthetics” and software fault can be tenuous. We may note in particular that the possibility for large data to overflow its assigned area is a fundamental source of security risks; and even pure user interface issues can become life-threatening in the case of critical applications such as air-traffic control.

Our second putative expert is right, however: no behavior is buggy unless it contradicts a specification. Where will the spec be in such an example? There are three possibilities, each with its limitations.

The first solution is to expect that in a carefully developed system every such property will have to be specified. This is conceivable, but hard, and the question arises of how to make sure nothing has been forgotten. Past  some threshold of criticality and effort, the only specifications that count are formal; there is not that much literature on specifying user interfaces formally, since much of the work on formal specifications has understandably concentrated on issues thought to be more critical.

Because of the tediousness of specifying such general properties again and again for each case, it might be better  — this is the second solution — to specify them globally, for an entire system, or for the user interfaces of an entire class of systems. Like any serious effort at specification, if it is worth doing, it is worth doing formally.

In either of these approaches the question remains of how we know we have specified everything of interest. This question, specification completeness, is not as hopeless as most people think; I plan to write an entry about it sometime (hint:  bing for “guttag horning”). Still, it is hard to be sure you did not miss anything relevant. Remember this the next time formal methods advocates — who should know better — tell you that with their techniques there “no longer is a need to test”, or when you read about the latest OS kernel that is “guaranteed correct and secure”. However important formal methods and proofs are, they can only guarantee satisfaction of the properties that the specifier has considered and stated. To paraphrase someone [1], I would venture that

Proofs can only show the absence of envisaged bugs, never rule out the presence of unimagined ones.

This is one of the reasons why tests will always, regardless of the progress of proofs, remain an indispensable part of the software development landscape [2]. Whatever you have specified and proved, you will still want to run the system (or, for certain classes of embedded software, some simulation of it) and see the results for yourself.

What then if we do not explicitly specify the desired property (as we did in the two approaches considered so far) but testing or actual operation still reveals some behavior that is clearly unsatisfactory? On what basis do we complain to the software’s producer? A solution here, the third in our list, might be to rely on generally accepted standards of professional development. This is common in other kinds of engineering: if you commission someone to build you a house, the contract may not explicitly state that the roof should not fall on your head while you are asleep; when this happens, you will still sue and accuse the builder of malpractice. Such remedies can work for software too, but the rules are murkier because we have not accepted, or even just codified, a set of general professional practices that would cover such details as “no display of information should overflow its assigned area”.

Until then I will remember to use one short tag a lot.

References

[1] Edsger W. Dijksra, Notes on Structured Programming, in Dahl, Dijkstra, Hoare, Structured Programming, Academic Press, 1972.

[2]  See Tests And Proofs (TAP) conference series, since 2007. The next conference, program-chaired by Angelo Gargantini and Gordon Fraser, will take place in the week of the TOOLS Federated Conferences in Málaga, Spain, in the week of June 28, 2010.

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Rejection letter classic

Part of the experience of being a scientist, in the industrial age of publication, is the rejection letter; especially the damning review whose author, anonymous of course, does not appear particularly competent. I have my own treasured collection, which I will publish one day. For a fiction so artfully designed as to be almost as good as the real thing, you can check  Simone Santini’s hilarious parody [1], a true classic.

Although there are a few references to it around the Web, I do not think it is as well known as it deserves to be. What Santini did was to imagine rejection letters for famous papers. He stated [2] that:

The reviews are a collage of reviews that I have seen of some papers (mine and of other people) that have been rejected because, I thought, the reviewer had completely misunderstood the paper. After a rejection at a database conference for what I thought were completely preposterous reasons, I had the idle thought that today even Codd’s paper on relational data bases (the foundation of the whole field) would never make it into a major data base conference…Many of the sentences that I use in the article are from actual reviews.

A sample from the imaginary Codd rejection letter:

E.F. CODD “A Relational Model of Data for Large Shared Data Banks.”  … The formalism is needlessly complex and mathematical, using concepts and notation with which the average data bank practitioner is unfamiliar. The paper doesn’t tell us how to translate its arcane operations into executable block access.

Adding together the lack of any real-world example, performance experiment, and implementation indication or detail, we are left with an obscure exercise using unfamiliar mathematics and of little or no practical consequence. It can be safely rejected.

All the others are gems too: Turing’s Entscheidungsproblem paper (“If the article is accepted, Turing should remember that the language of this journal is English and change the title accordingly”); Dijstra’s Goto considered harmful; Hoare’s 1969 axiomatic semantics paper (the author “should also extend the method to be applicable to a standard programming language such as COBOL or PL/I and provide the details of his implementation, possibly with a few graphics to show how the system works in practice”) etc.

To avoid a spoiler I will  cite no more;  you should read the paper if you do not know it yet. It rings so true.

References

[1] Simone Santini: We Are Sorry to Inform You …, in IEEE Computer, vol. 38, no. 12, pp. 128, 126-127, December 2005,  online on the IEEE site. There is also a copy here.

 [2] http://www.omlettesoft.com/newjournal.php3?who=Lord+Omlette&id=1134629858.

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“Touch of Class” published

My textbook Touch of Class: An Introduction to Programming Well Using Objects and Contracts [1] is now available from Springer Verlag [2]. I have been told of many bookstores in Europe that have it by now; for example Amazon Germany [3] offers immediate delivery. Amazon US still lists the book as not yet published [4], but I think this will be corrected very soon.

touch_of_class

The book results from six years of teaching introductory programming at ETH Zurich. It is richly illustrated in full color (not only with technical illustrations but with numerous photographs of people and artefacts). It is pretty big, but designed so that a typical one-semester introductory course can cover most of the material.

Many topics are addressed (see table of contents below), including quite a few that are seldom seen at the introductory level. Some examples, listed here in random order: a fairly extensive introduction to software engineering including things like requirements engineering (not usually mentioned in programming courses, with results for everyone to see!) and CMMI, a detailed discussion of how to implement recursion, polymorphism and dynamic binding and their role for software architecture, multiple inheritance, lambda calculus (at an introductory level of course), a detailed analysis of the Observer and Visitor patterns, event-driven programming, the lure and dangers of references and aliasing, topological sort as an example of both algorithm and API design, high-level function closures, software tools, properties of computer hardware relevant for programmers, undecidability etc.

The progression uses an object-oriented approach throughout; the examples are in Eiffel, and four appendices present the details of Java, C#, C++ and C. Concepts of Design by Contract and rigorous development are central to the approach; for example, loops are presented as a technique for computing a result by successive approximation, with a central role for the concept of loop invariant. This is not a “formal methods” book in the sense of inflicting on the students a heavy mathematical apparatus, but it uses preconditions, postconditions and invariants throughout to alert them to the importance of reasoning rigorously about programs. The discussion introduces many principles of sound design, in line with the book’s subtitle, “Learning to Program Well”.

The general approach is “Outside-In” (also known as “Inverted Curriculum” and described at some length in some of my articles, see e.g. [5]): students have, right from the start, the possibility of working with real software, a large (150,000-line) library that has been designed specifically for that purpose. Called Traffic, this library simulates traffic in a city; it is graphical and of good enough visual quality to be attractive to today’s “Wii generation” students, something that traditional beginners’ exercises, like computing the 7-th Fibonacci number, cannot do (although we have these too as well). Using the Traffic software through its API, students can right from the first couple of weeks produce powerful applications, without understanding the internals of the library. But they do not stop there: since the whole thing is available in open source, students learn little by little how the software is made internally. Hence the name “Outside-In”: understand the interface first, then dig into the internals. Two advantages of the approach are particularly worth noting:

  • It emphasizes the value of abstraction, and particular contracts, not by preaching but by showing to students that abstraction helps them master a large body of professional-level software, doing things that would otherwise be unthinkable at an introductory level.
  • It addresses what is probably today the biggest obstacle to teaching introductory programming: the wide diversity of initial student backgrounds. The risk with traditional approaches is either to fly too high and lose the novices, or stay too low and bore those who already have programming experience. With the Outside-In method the novices can follow the exact path charted from them, from external API to internal implementation; those who already know something about programming can move ahead of the lectures and start digging into the code by themselves for information and inspiration.

(We have pretty amazing data on students’ prior programming knowledge, as  we have been surveying students for the past six years, initially at ETH and more recently at the University of York in England thanks to our colleague Manuel Oriol; some day I will post a blog entry about this specific topic.)

The book has been field-tested in its successive drafts since 2003 at ETH, for the Introduction to Programming course (which starts again in a few weeks, for the first time with the benefit of the full text in printed form). Our material, such as a full set of slides, plus exercises, video recordings of the lectures etc. is available to any instructor selecting the text. I must say that Springer did an outstanding job with the quality of the printing and I hope that instructors, students, and even some practitioners already in industry will like both form and content.

Table of contents

Front matter: Community resource, Dedication (to Tony Hoare and Niklaus Wirth), Prefaces, Student_preface, Instructor_preface, Note to instructors: what to cover?, Contents

PART I: Basics
1 The industry of pure ideas
2 Dealing with objects
3 Program structure basics
4 The interface of a class
5 Just Enough Logic
6 Creating objects and executing systems
7 Control structures
8 Routines, functional abstraction and information hiding
9 Variables, assignment and references
PART II: How things work
10 Just enough hardware
11 Describing syntax
12 Programming languages and tools
PART III: Algorithms and data structures
13 Fundamental data structures, genericity, and algorithm complexity
14 Recursion and trees
15 Devising and engineering an algorithm: Topological Sort
PART IV: Object-Oriented Techniques
16 Inheritance
17 Operations as objects: agents and lambda calculus
18 Event-driven design
PART V: Towards software engineering
19 Introduction to software engineering
PART VI: Appendices
A An introduction to Java (from material by Marco Piccioni)
B An introduction to C# (from material by Benjamin Morandi)
C An introduction to C++ (from material by Nadia Polikarpova)
D From C++ to C
E Using the EiffelStudio environment
Picture credits
Index

References

[1] Bertrand Meyer, Touch of Class: An Introduction to Programming Well Using Objects and Contracts, Springer Verlag, 2009, 876+lxiv pages, Hardcover, ISBN: 978-3-540-92144-8.

[2] Publisher page for [1]: see  here. List price: $79.95. (The page says “Ships in 3 to 4 weeks” but I think this is incorrect as the book is available; I’ll try to get the mention corrected.)

[3] Amazon.de page: see here. List price: EUR 53.45 (with offers starting at EUR 41.67).

[4] Amazon.com page: see here. List price: $63.96.

[5] Michela Pedroni and Bertrand Meyer: The Inverted Curriculum in Practice, in Proceedings of SIGCSE 2006, ACM, Houston (Texas), 1-5 March 2006, pages 481-485; available online.

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One cheer for incremental research

[Note: an updated version of this article (June 2011) appears in the Communications of the ACM blog.]

The world of research funding, always a little strange, has of late been prey to a new craze: paradigm-shift mania. We will only fund twenty curly-haired cranky-sounding visionaries in the hope that one of them will invent relativity. The rest of you — bit-players! Petty functionaries! Slaves toiling at incremental research!  — should be ashamed of even asking.

Take this from the US National Science Foundation’s current description of funding for Computer Systems Research [1]:

CSR-funded projects will enable significant progress on challenging high-impact problems, as opposed to incremental progress on familiar problems.

 The European Research Council is not to be left behind [2]:

Projects being highly ambitious, pioneering and unconventional

Research proposed for funding to the ERC should aim high, both with regard to the ambition of the envisaged scientific achievements as well as to the creativity and originality of proposed approaches, including unconventional methodologies and investigations at the interface between established disciplines. Proposals should rise to pioneering and far-reaching challenges at the frontiers of the field(s) addressed, and involve new, ground-breaking or unconventional methodologies, whose risky outlook is justified by the possibility of a major breakthrough with an impact beyond a specific research domain/discipline.

Frontiers! Breakthrough! Rise! Aim high! Creativity! Risk! Impact! Pass me the adjective bottle. Ground-breaking! Unconventional! Highly ambitious! Major! Far-reaching! Pioneering! Galileo and Pasteur only please – others need not apply.

As everyone knows including the people who write such calls, this is balderdash. First, 99.97% of all research (precise statistic derived from my own ground-breaking research, further funding welcome) is incremental. Second, when a “breakthrough” does happen — the remaining 0.03%  — it was often not planned as a breakthrough.

Incremental research is a most glorious (I have my own supply of adjectives) mode of doing science. Beginning PhD students can be forgiven for believing the myth of the lone genius who penetrates the secrets of time and space by thinking aloud during long walks with his best friend [3]; we all, at some stage, shared that delightful delusion. But every researcher, presumably including those who go on to lead research agencies,  quickly grows up and learns that it is not how things happen. You read someone else’s solution to a problem, and you improve on it. Any history of science will tell you that for every teenager who from getting hit by a falling apple intuits the structure of the universe there are hundreds of great researchers who look at the state of the art and decide they can do a trifle better.

Here is a still recent example, particularly telling because we have the account from the scientist himself. It would not be much of an exaggeration to characterize the entire field of program proving over the past four decades as a long series of variations on Tony Hoare’s 1969 Axiomatic Semantics paper [4]. Here Hoare’s recollection, from his Turing Award lecture [5]:

In October 1968, as I unpacked my papers in my new home in Belfast, I came across an obscure preprint of an article by Bob Floyd entitled “Assigning Meanings to Programs.” What a stroke of luck! At last I could see a way to achieve my hopes for my research. Thus I wrote my first paper on the axiomatic approach to computer programming, published in the Communications of the ACM in October 1969.

(See also note [6].) Had the research been submitted for funding, we can imagine the reaction: “Dear Sir, as you yourself admit, Floyd has had the basic idea [7] and you are just trying to present the result better. This is incremental research; we are in the paradigm-shift business.” And yet if Floyd had the core concepts right it is Hoare’s paper that reworked and extended them into a form that makes practical semantic specifications and proofs possible. Incremental research at its best.

The people in charge of research programs at the NSF and ERC are themselves scientists and know all this. How come they publish such absurd pronouncements? There are two reasons. One is the typical academic’s fascination with industry and its models. Having heard that venture capitalists routinely fund ten projects and expect one to succeed, they want to transpose that model to science funding; hence the emphasis on “risk”. But the transposition is doubtful because venture capitalists assess their wards all the time and, as soon as they decide a venture is not going to break out, they cut the funding overnight, often causing the company to go under. This does not happen in the world of science: most projects, and certainly any project that is supposed to break new ground, gets funded for a minimum of three to five years. If the project peters out, the purse-holder will only realize it after spending all the money.

The second reason is a sincere desire to avoid mediocrity. Here we can sympathize with the funding executives: they have seen too many “here is my epsilon addition to the latest buzzword” proposals. The last time I was at ECOOP, in 2005, it seemed every paper was about bringing some little twist to aspect-oriented programming. This kind of research benefits no one and it is understandable that the research funders want people to innovate. But telling submitters that every project has to be epochal (surprisingly, “epochal” is missing from the adjectives in the descriptions above  — I am sure this will soon be corrected) will not achieve this result.

It achieves something else, good neither for research nor for research funding: promise inflation. Being told that they have to be Darwin or nothing, researchers learn the game and promise the moon; they also get the part about “risk” and emphasize how uncertain the whole thing is and how high the likelihood it will fail. (Indeed, since — if it works — it will let cars run from water seamlessly extracted from the ambient air, and with the excedent produce free afternoon tea.)

By itself this is mostly entertainment, as no one believes the hyped promises. The real harm, however, is to honest scientists who work in the normal way, proposing to bring an important contribution to the  solution of an important problem. They risk being dismissed as small-timers with no vision.

Some funding agencies have kept their heads cool. How refreshing, after the above quotes, to read the general description of funding by the Swiss National Science Foundation [8]:

The central criteria for evaluation are the scientific quality, originality and project methodology as well as qualifications and track record of the applicants. Grants are awarded on a competitive basis.

In a few words, it says all there is to say. Quality, originality, methodology, and track record. Will the research be “ground-breaking” or “incremental”? We will know when it is done.

I am convinced that the other agencies will come to their senses and stop the paradigm-shift nonsense. One reason for hope is in the very excesses of the currently fashionable style. The European Research Council quote includes, by my count, nineteen ways of saying that proposals must be daring. Now it is a pretty universal rule of life that someone who finds it necessary to say the same thing nineteen times in a single paragraph does not feel sure about it. He is trying to convince himself. At some point the people in charge will realize that such hype does not breed breakthroughs; it breeds more hype.

Until that happens there is something that some of us can do: refuse to play the game. Of course we are all convinced that our latest idea is the most important one ever conceived by humankind, and we want to picture it in the most favorable light. But we should resist the promise inflation. Such honesty comes at a risk. (I still remember a project proposal, many years ago, which came back with glowing reviews: the topic was important, the ideas right, the team competent. The agency officer’s verdict: reject. The proposers are certain to succeed, so it’s not research.) For some people, there is really no choice but to follow the lead: if your entire career depends on getting external funding, no amount of exhortation will prevent you from saying what the purse-holders want to hear. But those of us who do have a choice (that is to say, will survive even if a project is rejected) should refuse the compromission. We should present our research ideas for what they are.

So: one cheer for incremental research.

Wait, isn’t the phrase supposed to be “two cheers” [9]?

All right, but let’s go at it incrementally. One and one-tenth cheer for incremental research. 

References

 

[1]  National Science Foundation, Division of Computer and Network Systems: Computer Systems Research  (CSR), at http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=13385.

[2] European Research Council: Advanced Investigators Grant, at http://erc.europa.eu/index.cfmfuseaction=page.display&topicID=66.

[3] The Berne years; see any biography of Albert Einstein.

[4] C.A.R. Hoare: An axiomatic basis for computer programming, in Communications of the ACM, vol. 12, no 10, pages 576–580,583, October 1969.

[5] C.A.R. Hoare: The Emperor’s Old Clothes, in Communications of the ACM, vol. 24, no.  2, pages 75 – 83, February 1981.

[6] In the first version of this essay I wrote “Someone should celebrate the anniversary!”. Moshe Vardi, editor of Communications of the ACM, has informed me that the October 2009 issue will include a retrospective by Hoare on the 1969 paper. I cannot wait to see it.

[7] Robert W. Floyd: Assigning meanings to programs, in Proceedings of the American Mathematical Society Symposia on Applied Mathematics, vol. 19, pp. 19–31, 1967.

[8] Swiss National Science Foundation:  Projects – Investigator-Driven Research, at http://www.snf.ch/E/funding/projects/Pages/default.aspx. Disclosure: The SNSF kindly funds some of my research.

[9] E.M. Forster: Two Cheers for Democracy, Edward Arnold, 1951.

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