In case you haven’t heard about it yet, let me point you to FOSE, the Future Of Software Engineering [1] symposium in Zurich next week, organized by Sebastian Nanz. It is all made of invited talks; it is hard to think (with the possible exception of the pioneers’ conference [2]) of any previous gathering of so many software engineering innovators:
Barry Boehm
Manfred Broy
Patrick Cousot
Erich Gamma
Yuri Gurevich
Michael Jackson
Rustan Leino
David Parnas
Dieter Rombach
Joseph Sifakis
Niklaus Wirth
Pamela Zave
Andreas Zeller
The symposium is over two days. It is followed by a special event on “Eiffel at 25” which, as the rest of FOSE, is resolutely forward-looking, presenting a number of talks on current Eiffel developments, particularly in the areas of verification integrated in the development cycle (see “Verification As A Matter Of Course” [3]) and concurrent programming.
References
[1] Future Of Software Engineering (FOSE): symposium home page.
[2] Broy and Denert, editors: Software Pioneers, Springer, 2002. See publisher’s page.
[3] Verification As a Matter Of Course (VAMOC): an earlier entry of this blog.
The software world is not flat; it is multipolar. Gone are the days of one-site, one-team developments. The increasingly dominant model today is a distributed team; the place where the job gets done is the place where the appropriate people reside, even if it means that different parts of the job get done in different places.
This new setup, possibly the most important change to have affected the practice of software engineering in this early part of the millennium, has received little attention in the literature; and even less in teaching techniques. I got interested in the topic several years ago, initially by looking at the phenomenon of outsourcing from a software engineering perspective [1]. At ETH, since 2004, Peter Kolb and I, aided by Martin Nordio and Roman Mitin, have taught a course on the topic [2], initially called “software engineering for outsourcing”. As far as I know it was the first course of its kind anywhere; not the first course about outsourcing, but the first to explore the software engineering implications, rather than business or political issues. We also teach an industry course on the same issues [3], attended since 2005 by several hundred participants, and started, with Mathai Joseph from Tata Consulting Services, the SEAFOOD conference [4], Software Engineering Advances For Outsourced and Offshore Development, whose fourth edition starts tomorrow in Saint Petersburg.
After a few sessions of the ETH course we realized that the most important property of the mode of software development explored in the course is not that it involves outsourcing but that it is distributed. In parallel I became directly involved with highly distributed development in the practice of Eiffel Software’s development. In 2007 we renamed the ETH course “Distributed and Outsourced Software Engineering” (DOSE) to acknowledge the broadened scope. The topic is still new; each year we learn a little more about what to teach and how to teach it.
The 2007 session saw another important addition. We felt it was no longer sufficient to talk about distributed development, but that students should practice it. Collaboration between groups in Zurich and other groups in Zurich was not good enough. So we contacted colleagues around the world interested in similar issues, and received an enthusiastic response. The DOSE project is itself distributed: teams from students in different universities collaborate in a single development. Typically, we have two or three geographically distributed locations in each project group. The participating universities have been Politecnico di Milano (where our colleagues Carlo Ghezzi and Elisabetta di Nitto have played a major role in the current version of the project), University of Nijny-Novgorod in Russia, University of Debrecen in Hungary, Hanoi University of Technology in Vietnam, Odessa National Polytechnic in the Ukraine and (across town for us) University of Zurich. For the first time in 2010 a university from the Western hemisphere will join: University of Rio Cuarto in Argentina.
We have extensively studied how the projects actually fare (see publications [4-8]). For students, the job is hard. Often, after a couple of weeks, many want to give up: they have trouble reaching their partner teams, understanding their accents on Skype calls, agreeing on modes of collaboration, finalizing APIs, devising a proper test plan. Yet they hang on and, in most cases, succeed. At the end of the course they tell us how much they have learned about software engineering. For example I know few better way of teaching the importance of carefully documented program interfaces — including contracts — than to ask the students to integrate their modules with code from another team halfway around the globe. This is exactly what happens in industrial software development, when you can no longer rely on informal contacts at the coffee machine or in the parking lot to smooth out misunderstandings: software engineering principles and techniques come in full swing. With DOSE, students learn and practice these fundamental techniques in the controlled environment of a university project.
An example project topic, used last year, was based on an idea by Martin Nordio. He pointed out that in most countries there are some card games played in that country only. The project was to program such a game, where the team in charge of the game logic (what would be the “business model” in an industrial project) had to explain enough of their country’s game, and abstractly enough, to enable the other team to produce the user interface, based on a common game engine started by Martin. It was tough, but some of the results were spectacular, and these are students who will not need more preaching on the importance of specifications.
We are currently preparing the next session of DOSE, in collaboration with our partner universities. The more the merrier: we’d love to have other universities participate, including from the US. Adding extra spice to the project, the topic will be chosen among those from the ICSE SCORE competition [9], so that winning students have the opportunity to attend ICSE in Hawaii. If you are teaching a suitable course, or can organize a student group that will fit, please read the project description [10] and contact me or one of the other organizers listed on the page. There is a DOSE of madness in the idea, but no one, teacher or student, ever leaves the course bored.
References
[1] Bertrand Meyer: Offshore Development: The Unspoken Revolution in Software Engineering, in Computer (IEEE), January 2006, pages 124, 122-123. Available here.
[5] Bertrand Meyer and Marco Piccioni: The Allure and Risks of a Deployable Software Engineering Project: Experiences with Both Local and Distributed Development, in Proceedings of IEEE Conference on Software Engineering & Training (CSEE&T), Charleston (South Carolina), 14-17 April 2008, ed. H. Saiedian, pages 3-16. Preprint version available online.
[6] Bertrand Meyer: Design and Code Reviews in the Age of the Internet, in Communications of the ACM, vol. 51, no. 9, September 2008, pages 66-71. (Original version in Proceedings of SEAFOOD 2008 (Software Engineering Advances For Offshore and Outsourced Development, Lecture Notes in Business Information Processing 16, Springer Verlag, 2009.) Available online.
[7] Martin Nordio, Roman Mitin, Bertrand Meyer, Carlo Ghezzi, Elisabetta Di Nitto and Giordano Tamburelli: The Role of Contracts in Distributed Development, in Proceedings of SEAFOOD 2009 (Software Engineering Advances For Offshore and Outsourced Development), Zurich, June-July 2009, Lecture Notes in Business Information Processing 35, Springer Verlag, 2009. Available online.
[8] Martin Nordio, Roman Mitin and Bertrand Meyer: Advanced Hands-on Training for Distributed and Outsourced Software Engineering, in ICSE 2010: Proceedings of 32th International Conference on Software Engineering, Cape Town, May 2010, IEEE Computer Society Press, 2010. Available online.
At the ACM Symposium on Applied Computing (SAC) in Sierre last week, I gave a talk entitled “How you will be programming in 10 years”, describing a number of efforts by various people, with a special emphasis on our work at both ETH and Eiffel Software, which I think point to the future of software development. Several people have asked me for the slides, so I am making them available [1].
It occurred to me after the talk that the slogan “Verification As a Matter Of Course” (VAMOC) characterizes the general idea well. The world needs verified software, but the software development community is reluctant to use traditional heavy-duty verification techniques. While some of the excuses are unacceptable, others sources of resistance are justified and it is our job to make verification part of the very fabric of everyday software development.
My bet, and the basis of large part of both Eiffel and the ETH verification work, is that it is possible to bring verification to practicing developers as a natural, unobtrusive component of the software development process, through the tools they use.
The talk also broaches on concurrency, where many of the same ideas apply; CAMOC is the obvious next slogan.
Let me start, dear reader of this blog, by probing your view of equality, and also of assignment. Two questions:
Is a value x always equal to itself? (For the seasoned programmers in the audience: I am talking about a value, as in mathematics, not an expression, as in programming, which could have a side effect.)
In programming, if we consider an assignment
x := y
and v is the value of y before that assignment (again, this little detour is to avoid bothering with side effects), is the value of x always equal to v after the assignment?
Maybe I should include here one of these Web polls that one finds on newspaper sites, so that you can vote and compare your answer to the Wisdom of Crowds. My own vote is clear: yes to both. Equality is reflexive (every value is equal to itself, at any longitude and temperature, no excuses and no exceptions); and the purpose of assignment is to make the value of the target equal to the value of the source. Such properties are some of the last ramparts of civilization. If they go away, what else is left?
754 enters the picture
Now come floating-point numbers and the famous IEEE “754” floating-point standard [1]. Because not all floating point operations yield a result usable as a floating-point number, the standard introduces a notion of “NaN”, Not a Number; certain operations involving floating-point numbers may yield a NaN. The term NaN does not denote a single value but a set of values, distinguished by their “payloads”.
Now assume that the value of x is a NaN. If you use a programming language that supports IEEE 754 (as they all do, I think, today) the test in
ifx = xthen …
is supposed to yield False. Yes, that is specified in the standard: NaN is never equal to NaN (even with the same payload); nor is it equal to anything else; the result of an equality comparison involving NaN will always be False.
Assignment behavior is consistent with this: if y (a variable, or an expression with no side effect) has a NaN value, then after
x := y
the test x = y will yield False.
Before commenting further let me note the obvious: I am by no means a numerics expert; I know that IEEE 754 was a tremendous advance, and that it was designed by some of the best minds in the field, headed by Velvel Kahan who received a Turing Award in part for that success. So it is quite possible that I am about to bury myself in piles of ridicule. On the other hand I have also learned that (1) ridicule does not kill, so I am game; and more importantly (2) experts are often right but not always, and it is always proper to question their reasoning. So without fear let me not stop at the arguments that “the committee must have voted on this point and they obviously knew what they were doing” and “it is the standard and implemented on zillions of machines, you cannot change it now”. Both are true enough, but not an excuse to censor questions.
What are the criteria?
The question is: compatibility with an existing computer standard is great, but what about compatibility with a few hundred years of mathematics? Reflexivity of equality is something that we expect for any data type, and it seems hard to justify that a value is not equal to itself. As to assignment, what good can it be if it does not make the target equal to the source value?
The question of assignment is particularly vivid in Eiffel because we express the expected abstract properties of programs in the form of contracts. For example, the following “setter” procedure may have a postcondition (expressed by the ensure clause):
set_x (v: REAL)
— Set the value of x (an attribute, also of type REAL) the value of v. do
… x := v ensure x = v end
If you call this procedure with a NaN argument for a compiler that applies IEEE 754 semantics, and monitor contracts at run time for testing and debugging, the execution will report a contract violation. This is very difficult for a programmer to accept.
A typical example arises when you have an assignment to an item of an array of REAL values. Assume you are executing a [i] := x. In an object-oriented view of the world (as in Eiffel), this is considered simplified syntax for the routine call a.put (x, i). The postcondition is that a [i] = x. It will be violated!
The experts’ view
I queried a number of experts on the topic. (This is the opportunity to express my gratitude to members of the IFIP working group 2.5 on numerical software [2], some of the world’s top experts in the field, for their willingness to respond quickly and with many insights.) A representative answer, from Stuart Feldman, was:
If I remember the debate correctly (many moons ago), NaN represents an indefinite value, so there is no reason to believe that the result of one calculation with unclear value should match that of another calculation with unclear value. (Different orders of infinity, different asymptotic approaches toward 0/0, etc.)
Absolutely correct! Only one little detail, though: this is an argument against using the value True as a result of the test; but it is not an argument for using the value False! The exact same argument can be used to assert that the result should not be False:
… there is no reason to believe that the result of one calculation with unclear value should notmatch that of another calculation with unclear value.
Just as convincing! Both arguments complement each other: there is no compelling reason for demanding that the values be equal; and there is no compelling argument either to demand that they be different. If you ignore one of the two sides, you are biased.
What do we do then?
The conclusion is not that the result should be False. The rational conclusion is that True and False are both unsatisfactory solutions. The reason is very simple: in a proper theory (I will sketch it below) the result of such a comparison should be some special undefined below; the same way that IEEE 754 extends the set of floating-point numbers with NaN, a satisfactory solution would extend the set of booleans with some NaB (Not a Boolean). But there is no NaB, probably because no one (understandably) wanted to bother, and also because being able to represent a value of type BOOLEAN on a single bit is, if not itself a pillar of civilization, one of the secrets of a happy life.
If both True and False are unsatisfactory solutions, we should use the one that is the “least” bad, according to some convincing criterion . That is not the attitude that 754 takes; it seems to consider (as illustrated by the justification cited above) that False is somehow less committing than True. But it is not! Stating that something is false is just as much of a commitment as stating that it is true. False is no closer to NaB than True is. A better criterion is: which of the two possibilities is going to be least damaging to time-honored assumptions embedded in mathematics? One of these assumptions is the reflexivity of equality: come rain or shine, x is equal to itself. Its counterpart for programming is that after an assignment the target will be equal to the original value of the source. This applies to numbers, and it applies to a NaN as well.
Note that this argument does not address equality between different NaNs. The standard as it is states that a specific NaN, with a specific payload, is not equal to itself.
What do you think?
A few of us who had to examine the issue recently think that — whatever the standard says at the machine level — a programming language should support the venerable properties that equality is reflexive and that assignment yields equality.
Every programming language should decide this on its own; for Eiffel we think this should be the specification. Do you agree?
Some theory
For readers who like theory, here is a mathematical restatement of the observations above. There is nothing fundamentally new in this section, so if you do not like strange symbols you can stop here.
The math helps explain the earlier observation that neither True nor False is more“committing” than the other. A standard technique (coming from denotational semantics) for dealing with undefinedness in basic data types, is to extend every data type into a lattice, with a partial order relation meaning “less defined than”. The lattice includes a bottom element, traditionally written “⊥” (pronounced “Bottom”) and a top element written ⊤ (“Top”). ⊥ represents an unknown value (not enough information) and ⊤ an error value (too much information). Pictorially, the lattice for natural numbers would look like this:
The lattice of integers
On basic types, we always use very simple lattices of this form, with three kinds of element: ⊥, less than every other element; ⊤, larger than all other elements; and in-between all the normal values of the type, which for the partial order of interest are all equal. (No, this is not a new math in which all integers are equal. The order in question simply means “is less defined than”. Every integer is as defined as all other integers, more defined than ⊥, and less defined than ⊤.) Such lattices are not very exciting, but they serve as a starting point; lattices with more interesting structures are those applying to functions on such spaces — including functions of functions —, which represent programs.
The modeling of floating-point numbers with NaN involves such a lattice; introducing NaN means introducing a ⊥ value. (Actually, one might prefer to interpret NaN as ⊤, but the reasoning transposes immediately.) More accurately, since there are many NaN values, the lattice will look more like this:
The lattice of floats in IEEE 754
For simplicity we can ignore the variety of NaNs and consider a single ⊤.
Functions on lattices — as implemented by programs — should satisfy a fundamental property: monotonicity. A function f is monotone (as in ordinary analysis) if, whenever x ≤ y, then f (x) ≤ f (y). Monotonicity is a common-sense requirement: we cannot get more information from less information. If we know less about x than about y, we cannot expect that any function (with a computer, any program) f will, out of nowhere, restore the missing information.
Demanding monotonicity of all floating-point operations reflects this exigency of monotonicity: indeed, in IEEE 754, any arithmetic operation — addition, multiplication … — that has a NaN as one of its arguments must yield a Nan as its result. Great. Now for soundness we should also have such a property for boolean-valued operations, such as equality. If we had a NaB as the ⊥ of booleans, just like NaN is the ⊥ of floating-point numbers, then the result of NaN = NaN would be NaB. But the world is not perfect and the IEEE 754 standard does not govern booleans. Somehow (I think) the designers thought of False as somehow less defined than True. But it is not! False is just as defined as True in the very simple lattice of booleans; according to the partial order, True and False are equal for the relevant partial order:
The lattice of booleans
Because any solution that cannot use a NaB will violate monotonicity and hence will be imperfect, we must resort to heuristic criteria. A very strong criterion in favor of choosing True is reflexivity — remaining compatible with a fundamental property of equality. I do not know of any argument for choosing False.
The Spartan approach
There is, by the way, a technique that accepts booleans as we love them (with two values and no NaB) and achieves mathematical rigor. If operations involving NaNs truly give us pimples, we can make any such operation trigger an exception. In the absence of ⊥ values, this is an acceptable programming technique for representing undefinedness. The downside, of course, is that just about everywhere the program must be ready to handle the exception in some way.
It is unlikely that in practice many people would be comfortable with such a solution.
Final observations
Let me point out two objections that I have seen. Van Snyder wrote:
NaN is not part of the set of floating-point numbers, so it doesn’t behave as if “bottom” were added to the set.
Interesting point, but, in my opinion not applicable: ⊥ is indeed not part of the mathematical set of floating point numbers, but in the form of NaN it is part of the corresponding type (float in C, REAL in Eiffel); and the operations of the type are applicable to all values, including NaN if, as noted, we have not taken the extreme step of triggering an exception every time an operation uses a NaN as one of its operands. So we cannot free ourselves from the monotonicity concern by just a sleight of hands.
Another comment, also by Van Snyder (slightly abridged):
Think of [the status of NaN] as a variety of dynamic run-time typing. With static typing, if x is an integer variable and y
x := y
does not inevitably lead to
x = y
True; and a compelling argument to require that conversions satisfy equality as a postcondition! Such reasoning — reflexivity again — was essential in the design of the Eiffel conversion mechanism [3], which makes it possible to define conversions between various data types (not just integers and reals and the other classical examples, but also any other user types as long as the conversion does not conflict with inheritance). The same conversion rules apply to assignment and equality, so that yes, whenever the assignment x := y is permitted, including when it involves a conversion, the property x = y is afterwards always guaranteed to hold.
It is rather dangerous indeed to depart from the fundamental laws of mathematics.
References
[1] IEEE floating-point standard, 754-2008; see summary and references in the Wikipedia entry.
[2] IFIP Working Group 2.5 on numerical software: home page.
(This entry originated as a post on the EiffelStudio user group mailing list.)
Here are a couple of actual examples of the new loop variants discussed in the blog entry immediately preceding this one. They came out of my current work; I started updating a program to take advantage of the new facility.
As a typical example, I replaced
local eht: HASH_TABLE [EXPRESSION, EXPRESSION] do … from eht := item (e) eht.start until eht.off loop Result.extend (eht.key_for_iteration) eht.forth end
by
acrossitem (e) asehtloopResult.extend (eht.key) end
which also gets rid of the local variable declaration. The second form is syntactic sugar for the first, but I find it justified.
Another case, involving nested loops:
— Previously: from other.start until other.off loop oht := other.item_for_iteration e := other.key_for_iteration from oht.start until oht.off loop put (e, oht.item_for_iteration) oht.forth end other.forth end
— Now:
acrossotherasoloop acrosso.itemasohtloopput (o.key, oht.item) end end
here getting rid of two local variable declarations (although I might for efficiency reintroduce the variable e to compute o.key just once).
It is important to note that these are not your grandmother’s typical loops: they iterate on complex data structures, specifically hash tables where the keys are lists and the items are themselves hash tables, with lists as both items and keys.
The mechanism is applicable to all the relevant data structures in EiffelBase (in other words, no need for the programmer to modify anything, just apply the across loop to any such structure), and can easily extended to any new structure that one wishes to define. In the short term at least, I still plan in my introductory teaching to show the explicit variants first, as it is important for beginners to understand how a loop works. (My hunch based on previous cases is that after a while we will feel comfortable introducing the abstract variants from the start, but it takes some time to learn how to do it right.)
New variants of the loop construct have been introduced into Eiffel, allowing a safer, more concise and more abstract style of programming. The challenge was to remain compatible with the basic loop concept, in particular correctness concerns (loop invariant and loop variant), to provide a flexible mechanism that would cover many different cases of iteration, and to keep things simple.
Here are some examples of the new forms. Consider a structure s, such as a list, which can be traversed in sequence. The following loop prints all elements of the list:
acrosssasc loopprint (c.item) end
(The procedure print is available on all types, and can be adapted to any of them by redefining the out feature; item gives access to individual values of the list.) More about c in just a moment; in the meantime you can just consider consider that using “asc” and manipulating the structure through c rather than directly through s is a simple idiom to be learned and applied systematically for such across loops.
The above example is an instruction. The all and some variants yield boolean expressions, as in
across sascallc.item > 0end
which denotes a boolean value, true if and only if all elements of the list are positive. To find out if at least one is positive, use
across sascsome c.item > 0end
Such expressions could appear, for example, in a class invariant, but they may be useful in many different contexts.
In some cases, a from clause is useful, as in
across sascfromsum := 0 loop sum := sum + c.index ∗ c.itemend
— Computes Σ i * s [i]
The original form of loop in Eiffel is more explicit, and remains available; you can achieve the equivalent of the last example, on a suitable structure, as
A list and a cursor
from sum := 0 ; s.start until s.after loop sum := sum + s.index ∗ s.item
s.forth end
which directly manipulates a cursor through s, using start to move it to the beginning, forth to advance it, and after to test if it is past the last element. The forms with across achieve the same purpose in a more concise manner. More important than concision is abstraction: you do not need to worry about manipulating the cursor through start, forth and after. Under the hood, however, the effect is the same. More precisely, it is the same as in a loop of the form
from sum := 0 ; c.start until c.after loop sum := sum + c.index ∗ c.item
c.forth end
wherec is a cursor object associated with the loop. The advantage of using a cursor is clear: rather than keeping the state of the iteration in the object itself, you make it external, part of a cursor object that, so to speak, looks at the list. This means in particular that many traversals can be active on the same structure at the same time; with an internal cursor, they would mess up with each other, unless you manually took the trouble to save and restore cursor positions. With an external cursor, each traversal has its own cursor object, and so does not interfere with other traversals — at least as long as they don’t change the structure (I’ll come back to that point).
With the across variant, you automatically use a cursor; you do not have to declare or create it: it simply comes as a result of the “asc” part of the construct, which introduces c as the cursor.
On what structures can you perform such iterations? There is no limitation; you simply need a type based on a class that inherits, directly or indirectly, from the library class ITERABLE. All relevant classes from the EiffelBase library have been updated to provide this inheritance, so that you can apply the across scheme to lists of all kinds, hash tables, arrays, intervals etc.
One of these structures is the integer interval. The notation m |..| n, for integers m and n, denotes the corresponding integer interval. (This is not a special language notation, simply an operator, |..|, defined with the general operator mechanism as an alias for the feature interval of INTEGER classes.) To iterate on such an interval, use the same form as in the examples above:
acrossm |..| nascfromsum := 0 loop sum := sum + a [c.item] end
— Computes Σ a [i], for i ranging from m to n, for an array (or other structure) a.
The key feature in ITERABLE is new_cursor, which returns a freshly created cursor object associated with the current structure. By default it is an ITERATION_CURSOR, the most general cursor type, but every descendant of ITERABLE can redefine the result type to something more specific to the current structure. Using a cursor — c in the above examples —, rather than manipulating the structure s directly, provides considerable flexibility thanks to the property that ITERATION_CURSOR itself inherits from ITERABLE and hence has all the iteration mechanisms. For example you may write
across s.new_cursor.reversedascloop print (c.item) end
to print elements in reverse order. (Using Eiffel’s operator mechanism, you may write –s.new_cursor, with a minus operator, as a synonym fornew_cursor.reversed.) The function reversed gives you a new cursor on the same target structure, enabling you to iterate backwards. Or you can use
across s.new_cursor + 3 ascloop print (c.item) end
(using s.new_cursor.incremented (3) rather than s.new_cursor + 3 if you are not too keen on operator syntax) to iterate over every third item. A number of other possibilities are available in the cursor classes.
A high-level iteration mechanism is only safe if you have the guarantee that the structure remains intact throughout the iteration. Assume you are iterating through a structure
acrosss ascloop some_routineend
and some_routine changes the structure s: the whole process could be messed up. Thanks to Design by Contract mechanisms, the library protects you against such mistakes. Features such as item and index, accessing properties of the structure during the iteration, are equipped with a precondition clause
require is_valid
and every operation that changes the structure sets is_valid to false. So as soon as any change happens, you cannot continue the iteration; all you can do is restart a new one; the command start, used internally to start the operation, does not have the above precondition.
Sometimes, of course, you do want to change a structure while traversing it; for example you may want to add an element just to the right of the iteration position. If you know what you are doing that’s fine. (Let me correct this: if you know what you are doing, express it through precise contracts, and you’ll be fine.) But then you should not use the abstract forms of the loop, across…; you should control the iteration itself through the basic form from … until … with explicit cursor manipulation, protected by appropriate contracts.
The two styles, by the way, are not distinct constructs. Eiffel has always had only one form of loop and this continues the case. The across forms are simply new possibilities added to the classical loop construct, with obvious constraints stating for example that you may not have both a some or all form and an explicit loop body. In particular, an across loop can still have an invariant clause , specifying the correctness properties of the loop, as in
across sascfromsum := 0 invariant sum = sigma (s, index) loop sum := sum + c.index ∗ c.itemend
EiffelStudio 6.5 already included the language update; the library update (not yet including the is_valid preconditions for data structure classes) will be made available this week.
These new mechanisms should increase the level of abstraction and the reliability of loops, a fundamental element of almost all programs.
In a previous post I briefly mentioned some work that I am doing on aliasing. There is a draft paper [1], describing the theory, calculus, graphical notation (alias diagrams) and implementation. Here I will try to give an idea of what it’s about, with the hope that you will be intrigued enough to read the article. Even before you read it you might try out the implementation[2], a simple interactive interface with all the examples of the article .
What the article does not describe in detail — that will be for a companion paper— is how the calculus will be used as part of a general framework for developing object-oriented software proved correct from the start, the focus of our overall “Trusted Components” project’ [3]. Let me simply state that the computation of aliases is the key missing step in the effort to make correctness proofs a standard part of software development. This is a strong claim which requires some elaboration, but not here.
The alias calculus asks a simple question: given two expressions representing references (pointers), can their values, at a given point in the program, ever reference the same object during execution?
As an example application, consider two linked lists x and y, which can be manipulated with operations such as extend, which creates a new cell and adds it at the end of the list:
The calculus makes it possible to prove that if x and y are not aliased to each other, then none of the pointers in any of the cells in either of the lists can point to (be aliased to) any cell of the other. If x is initially aliased to y, the property no longer holds. You can run the proof (examples 18 and 19) in the downloadable implementation.
The calculus gives a set of rules, each applying to a particular construct of the language, and listed below.
The rule for a construct p is of the form a |=p= a’
where a and a’ are alias relations; this states that executing p in a state where the alias relation is a will yield the alias relation a’ in the resulting state. An alias relation is a symmetric, irreflexive relation; it indicates which expressions and variables can be aliased to each other in a given state.
The constructs p considered in the discussion are those of a simplified programming language; a modern object-oriented language such as Eiffel can easily be translated into that language. Some precision will be lost in the process, meaning that the alias calculus (itself precise) can find aliases that would not exist in the original program; if this prevents proofs of desired properties, the cutinstruction discussed below serves to correct the problem.
The first rule is for the forget instruction (Eiffel: x := Void): a |=forgetx= a \- {x}
where the \- operator removes from a relation all the elements belonging to a given set A. In the case of object-oriented programming, with multidot expressions x.y.z, the application of this rule must remove all elements whose first component, here x, belongs to A.
The rule for creation is the same as for forget:
a |=createx= a \- {x}
The two instructions have different semantics, but the same effect on aliasing.
The calculus has a rule for the cut instruction, which removes the connection between two expressions:
a |=cut x, y= a — <x, y>
where — is set difference and <x, y> includes the pairs [x, y] and [y, x] (this is a special case of a general notation defined in the article, using the overline symbol). The cut instruction corresponds, in Eiffel, to cut x /= y end: a hint given to the alias calculus (and proved through some other means, such as standard axiomatic semantics) that some references will not be aliased.
The rule for assignment is
a |= (x := y) = givenb = a \- {x} then <bÈ {x} x (b / y)}> end
whereb /y (“quotient”), similar to an equivalence class in an equivalence relation, is the set of elements aliased to y in b, plus y itself (remember that the relation is irreflexive). This rule works well for object-oriented programming thanks to the definition of the \- operator: in x := x.y, we must not alias x to x.y, although we must alias it to any z that was aliased to x.y.
The paper introduces a graphical notation, alias diagrams, which makes it possible to reason effectively about such situations. Here for example is a diagram illustrating the last comment:
Alias diagram for a multidot assignment
(The grayed elements are for explanation and not part of the final alias relation.)
For the compound instruction, the rule is:
a |= (p ; q) = (a |= p) |= q)
For the conditional instruction, we get:
a |= (thenpelseq end) = (a |= p) È (a |= q)
Note the form of the instruction: the alias calculus ignores information from the then clause present in the source language. The union operator is the reason why alias relations, irreflexive and symmetric, are not necessarily transitive.
The loop instruction, which also ignores the test (exit or continuation condition), is governed by the following rule:
a |= (loop pend) = tN
where span style=”color: #0000ff;”>N is the first value such that tN = tN+1 (in other words, tN is the fixpoint) in the following sequence:
t0 = a tn+1= (tn È (tn |= p))
The existence of a fixpoint and the correctness of this formula to compute it are the result of a theorem in the paper, the “loop aliasing theorem”; the proof is surprisingly elaborate (maybe I missed a simpler one).
For procedures, the rule is
a |= call p = a |= p.body
where p.body is the body of the procedure. In the presence of recursion, this gives rise to a set of equations, whose solution is the fixpoint; again a theorem is needed to demonstrate that the fixpoint exists. The implementation directly applies fixpoint computation (see examples 11 to 13 in the paper and implementation).
The calculus does not directly consider routine arguments but treats them as attributes of the corresponding class; so a call is considered to start with assignments of the form f : = a for every pair of formal and actual arguments f and a. Like the omission of conditions in loops and conditionals, this is a source of possible imprecision in translating from an actual programming language into the calculus, since values passed to recursive activations of the same routine will be conflated.
Particularly interesting is the last rule, which generalizes the previous one to qualified calls of the form x. f (…) as they exist in object-oriented programming. The rule involves the new notion of inverse variable, written x’ where x is a variable. Laws of the calculus (with Current denoting the current object, one of the fundamental notions of object-oriented programming) are
Current.x = x
x.Current = x x.x’ = Current x’.x = Current
In other words, Current plays the role of zero element for the dot operator, and variable inversion is the inverse operation. In a call x.f, where x denotes the supplier object (the target of the call), the inverse variable provides a back reference to the client object (the caller), indispensable to interpret references in the original context. This property is reflected by the qualified client rule, which uses the auxiliary operator n (where x n a, for a relation a and a variable x, is the set of pairs [x.u, y.v] such that the pair [u, v] is in a). The rule is:
a |= callx.r = x n ((x’n a ) |= callr)
You need to read the article for the full explanation, but let me offer the following quote from the corresponding section (maybe you will note a familiar turn of phrase):
Thus we are permitted to prove that the unqualified call creates certain aliasings, on the assumption that it starts in its own alias environment but has access to the caller’s environment through the inverted variable, and then to assert categorically that the qualified call has the same aliasings transposed back to the original environment. This change of environment to prove the unqualified property, followed by a change back to the original environment to prove the qualified property, explains well the aura of magic which attends a programmer’s first introduction to object-oriented programming.
I hope you will enjoy the calculus and try the examples in the implementation. It is fun to apply, and there seems to be no end to the potential applications.
Reference
[1] Bertrand Meyer: The Theory and Calculus of Aliasing, draft paper, first published 12 January 2009 (revised 21 January 2010), available here and also at arxiv.org.
[2] Implementation (interactive version to try all the examples of the paper): downloadable Windows executable here.
[3] Bertrand Meyer: The Grand Challenge of Trusted Components, in 2003 International Conference on Software Engineering, available here.
In the past few weeks I wrote a program to compute the aliases of variables and expressions in an object-oriented program (based on a new theory [1]).
For one of the data structures, I needed a specific notion of equality, so I did the standard thing in Eiffel: redefine the is_equal function inherited from the top class ANY, to implement the desired variant.
The first time I ran the result, I got a postcondition violation. The violated postcondition clauses was not even any that I wrote: it was an original postcondition of is_equal (other:likeCurrent) in ANY, which my redefinition inherited as per the rules of Design by Contract; it reads
symmetric: Resultimpliesother ~ Current
meaning: equality is symmetric, so if Result is true, i.e. the Current object is equal to other, then other must also be equal to Current. (~ is object equality, which applies the local version is is_equal). What was I doing wrong? The structure is a list, so the code iterates on both the current list and the other list:
from start ; other.start ; Result := True until (notResult) orafterloop ifother.afterthenResult := Falseelse Result := (item ~ other.item) forth ; other.forth end end
Simple enough: at each position check whether the item in the current list is equal to the item in the other list, and if so move forth in both the current list and the other one; stop whenever we find two unequal elements, or we exhaust either list as told by after list. (Since is_equal is a function and not produce any side effect, the actual code saves the cursors before the iteration and restores them afterwards. Thanks to Ian Warrington for asking about this point in a comment to this post. The new across loop variant described in two laterpostings uses external cursors and manages them automatically, so this business of maintaining the cursor manually goes away.)
The problem is that with this algorithm it is possible to return True if the first list was exhausted but not the second, so that the first list is a subset of the other rather than identical. The correction is immediate: add
Result and other_list.after
after the loop; alternatively, enclose the loop in a conditional so that it is only executed if count = other.count (this solution is better since it saves much computation in cases of lists of different sizes, which cannot be equal).
The lesson (other than that I need to be more careful) is that the error was caught immediately, thanks to a postcondition violation — and one that I did not even have to write. Just another day at the office; and let us shed a tear for the poor folks who still program without this kind of capability in their language and development environment.
Reference
[1] Bertrand Meyer: The Theory and Calculus of Aliasing, draft paper, available here.
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.
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 Objectsand 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.
A spectre is haunting programming — the spectre of null-pointer dereferencing. All the programming languages of old Europe and the New World have entered into a holy alliance to make everyone’s programs brittle: Java, C, Pascal, C++, C# and yes, until recently, Eiffel.
The culprit is the use of references to denote objects used in calls: in
x.f (...)
the value of x is a reference, which normally denotes an object but could at any time be void (or “null”). If this happens, the resulting “void call” will cause an exception and, usually, a crash. No amount of testing can remove the risk entirely; the only satisfactory solution is a static one, enforcing void safety at the language level.
To this end, Eiffelists of various nationalities have assembled in the Cloud and sketched the following manifesto, to be published in the English language:
Avoid a Void: The Eradication of Null Dereferencing
Bertrand Meyer, Alexander Kogtenkov, Emmanuel Stapf
White paper available here.
