Worth Reading

While I'm working on my next big post, here are a few things worth reading.

Scott Rosenberg's post on ambiguity was right on. Ambiguity is a double edged sword - it can make things elegant, or intractable. Scott's insight is very sharp, as usual.

Last year, Basil Vandegriend put out a concise and helpful post on writing good unit tests. Most people agree tests are important, but many do not know precisely how to make them work. Basil addresses real issues, and gives good advice. I wish I had read this ten years ago.

Basil's latest post on the top five essential practices for writing software is also bang on. It is a quick must read for programmer trying to make the leap from just coding to professional software development.
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Code Read 5 - Knuth's "Structured Programming with Go Tos"

Code Reads 5 takes us from Dijkstra to Knuth, and his humorously titled "Structured Programming with Go To Statements". In it, Knuth addresses how the field seems to have missed the real point of Dijkstra's structured programming, and instead focused on mindlessly eliminating "go to" statements. Knuth quotes Hoare when saying the most important point is "the systematic use of abstraction to control a mass of detail", not eliminating a particular programming tool.

The main topic of Knuth's article is not abstraction, but rather examining the uses of "go to" that improve a program, and how newer (in 1974) language constructs (like break statements and case statements) can almost always be used to express the meaning of those "go to" statements. In fact, he ends by saying that although he would personally like to keep "go to" available in higher level languages, he would probably never need to use it.

In general, this piece feels a bit dated, which is a measure of its own success - Knuth said that his aim was to put the "go to" controversy to rest by showing it to be moot, which, except for a few lifelong partisans, is where it is now. And many of the structures he discusses (using break to exit from loops, early versions of case statements) are common in almost all languages. So it makes a fitting end to Code Read's exploration of the roots of language semantics for abstraction.

What I found most interesting was his study of optimization, which the process of changing a program so that it does its work more efficiently. Almost all are examples of optimization. Here he makes some very relevant points, but I think one of his observations is particularly dated.

His most important point is something which many beginning programmers still do not understand: "Premature optimization is the root of all evil". We should write our programs in the clearest way, he says, so they will almost certainly be correct. Then, if there are performance problem, we should analyze the code to find where those problems are, and only optimize those sections. Optimizing first is a surefire way to render a program difficult to understand and likely to contain bugs.

He goes to to give some of good examples of fine grain optimization technique, things that all programmers should be aware of, but will only rarely be used.

Where I feel his view has become outdated is how he relates to small optimizations. "In established engineering disciplines a 12% improvement, easily obtained, is never considered marginal". I think this is no longer true for computer science.

People often ask why building software is not like building bridges. This is one reason. Nobody expects a footbridge to carry a truck. Yet we routinely use the same software to handle hundreds of items that we use to handle hundreds of millions of items. So while a 12% improvement in bridge strength is something meaningful, a 12% improvement in software performance is not nearly so impressive. (In very specific cases, it might be meaningful, but generally its not.)

Suppose you're writing part of a program which is interactive - that is a person will be waiting for the result. And suppose that it takes 60 seconds. A 12 percent improvement is just over 7 seconds, which means the optimized code still takes 52 seconds. Still too long to wait, and not long enough to get a cup of coffee. In fact, I doubt most people will notice the difference, since we are much more susceptible to psychological factors when waiting for computers. (Just one example of this.)

In Knuth's day, people had a different relationship with computers, so this kind of performance gain was more relevant. Not so today. In fact, these days algorithm performance is typically described using "big O notation", which loosely quantifies how an algorithm works as the size of its input changes. And it provides what is by and large a more meaningful estimate of the performance of an algorithm.

To understand this, it is helpful to use example. Suppose we want to compare three ways of sorting a list containing 1000n names (so for 1000 names n = 1, for 2000 names n = 2, etc). We analyze the algorithms as Knuth did in his paper, and come up with the following formulas. The first method takes take 6(2ⁿ) milliseconds, the second takes 3(2ⁿ) + 15n milliseconds, and the third takes 25n² milliseconds. From a simple test of 1000 names, with n=1, we get:

Method 1: 12 milliseconds.
Method 2: 21 milliseconds.
Method 3: 25 milliseconds.


We might decide that method 1 is the best say to go. But we'd be wrong, if we wanted to sort bigger lists. Using big O notation makes that clear.

In big O notation, we ignore any constant multiplication, and only take the most rapidly increasing term. So we say method 1 is O(2ⁿ), method 2 is also O(2ⁿ), and method 3 is O(n²). This is the essential information about which is faster, and since 2ⁿ is much larger than n², for large n, we know that the third technique is actually the fastest in general. For example, when n=10:

Method 1: 6.1 seconds.
Method 2: 3.2 seconds.
Method 3: 2.5 seconds.

This is exactly reversed from what we had before - method 3 is the fastest and method 1 is the slowest. And things get much worst for methods 1 and 2 when n=100:

Method 1: 240,000,000,000,000,000,000 years
Method 2: 120,000,000,000,000,000,000 years
Method 3: 250 seconds

At this scale methods 1 and 2 are completely useless, leaving method 3 as the only option.

To tie all of this back to Knuth's paper, almost all of his cases for the use of "go to" statements involve optimizations which do not change the big O performance of program at all. So while there are programs out there where this is important (certain key inner loops in operating systems or scientific software) most of us will always be able to rely in library calls where someone else has already does this kind of super-tight optimization, and we should focus solely on selecting the appropriate abstractions for our algorithm. That is, we need to select abstractions that give us the best big O performance. And using "go to" or not using "go to" has nothing to do with this kind of optimization.
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Code Read 4 - Dijkstra's Notes Part Two

Edsgar W. Dijkstra's "Notes on Structured Programming" is definitely a meal. Its quite a lot for one Code Read. So I broke it into two parts. First, we had the appetizers, now here's the main course.

Program families and evolving software

Dijkstra points out that programs exist in large families of similar programs. When we make changes, we are transforming it from one member of the family to another. By thinking of programs in this way, the importance of a programs structure becomes even more important - because we would like the families to share not just code, but also correctness. If the structure is confusing, the changing the program is difficult because lots of code changes and that code all needs to have its correctness reexamined. A simply structured program tends to require changes in areas that are already well-isolated, thus less code changes, and we need to think less about the correctness of the new code and the code that depends on it. (Similarly, although Dijkstra does not make this point explicitly, a layered structure can make it more clear which areas rely on the changed code, so they can also be verified easily.)

Moreover, Dijkstra points out, from the structure of a program we can understand not just how it works, but also what kind of changes will be easy to make - what other members of its family are close. This stuck me as another important point, since a great deal of time and effort is spent managing and responding to change.

Specifying clarity

Starting to get to the meat of his subject, Dijkstra spends a chapter discussing subroutines, or what has come to be called "structured programming". He sets out to avoid "motherhood" statements that are unobjectionable but hopelessly vague, and to be specific about what makes clear, easy to understand, and easy to modify programming.

Leaving aside his discussions of the fine points programming semantics, he makes several key arguments about subroutines:

• subroutines should not be used to simply shorten code, but rather to create a reliable abstraction
• properly used, they become helpful in limiting the scope of changes, by allowing us to replace the implementation of a subroutine with a different implementation
  
• they help clarify at a particular moment in time which associations are still valid between the state of the machine and the meaning we assign to that state
  
• they allow work to be divided into small units without having to re-invent the wheel for each unit
  

What is most relevant about this for us is not necessarily the application of these ideas to subroutines, but to any software design construct - objects, aspects, models, etc. Many novice programmers get so excited about a particular technique like Object Oriented programming, that the miss the fundamental reasons for using it in the first place - which Dijkstra has helfuly laid bare for us.

Also its important to note that Dijkstra is not describing the "lego-like" building block we'd all like to have, and which we may never get. He never describes having a large library of such objects and simply selecting and combining them to build programs. When he does refer to such "lego-like" tools, he only mentions the most basic of abstractions, things like "integer". And he seems to confine these largely to the realm of predefined hardware and language constructs:

"although these facilities have to be provided in some form or another - providing these facilities falls outside the scope of the programmer's responsibility and also that the programmer will accept any reasonable implementation of them."

In order words, we should not be too picky about our tools, since these tools will probably be equally suited to our task. Although certainly there are cases where this is untrue, the message seems to be that there are general libraries available for the basic things we do as programmers, and that baring specific needs, one will work as well as another. But Dijkstra says nothing about more complex libraries of building blocks - instead he introduces, in his next section, the image of a string of pearls.

The string of pearls

Having built his argument carefully, Dijkstra comes to his grandest image - the layers of abstraction in a program as a string of pearls.

In this metaphor, designing a program becomes a process of creating (at least intellectually) a somewhat larger set of pearls than we need, and then selecting the ones that we will finally use to build our program. Other programs in the same family would use a different subset of pearls, in a different order.

When we need to modify a program, we can replace a pearl, and some of those below it, with a new set of pearls. Again, Dijkstra is not simple enough to suggest that one could simply replace one pearl with another, and that everything would work out. Instead, he saw that along the string there are various concepts used by the pearls, and many of which will be shared among different pearls. Changing those concepts will require replacing all of the pearls that use that concept.

By looking at how many concepts span which pearls, one can get a sense of the complexity of a particular program (or design) - more complex program will have "thicker" and "longer" weaves of concepts. Such thick programs will be more difficult to create, understand, and debug, because they require more mental work for us to understand all of the pieces woven together. Thinner weaves are easier to understand, since there is less to hold in our heads at one time.

Dijkstra's image is not the image of massively reusable bits of code, but rather a way to think of the complexity of a program - almost to measure it - and a way to compare alternatives. And the central concept of this, as in almost all of Dijkstra's writings that we've read in Code Reads is this - simplicity is brought about by isolation of details through abstraction.

Its quite an important idea. Almost every development in software design techniques since then has been an attempt to provide this isolation and abstraction. And it has been very successful, in that we now regularly write working programs tens or hundred of times as long and complex as what Dijkstra was talking about. Of course, sometimes they do not work, so lets see what comes next in Code Reads.
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Code Read 3 - The Humble Dijkstra

The third Code Read that Scott Rosenberg chose was another Edsgar Dijkstra essay - this one called "The Humble Programmer". Vastly oversimplifying, Dijkstra is making this very important point: despite all of our achievements, we are limited creatures, and our intellect can easily be overwhelmed by our own creations. Particularly as access to computing power increases, and our expectations of its ability increases, our current approach to software will lead us into an inescapable swamp of unmaintainable and horrendously expensive computer systems.

More than thirty years have passed since he said this, yet we are still wandering around the edge of that swamp. Dijkstra does give us a way out - his argument: an appropriate understanding of the system we are building will make it easy to build and maintain. Furthermore, we have the tools to achieve this understanding.

The most important point, he says, is to "...confine ourselves to the design and implementation of intellectually manageable programs".

After reading the comments at Code Read 3, I think this point created some misunderstanding, which can easily lead people to miss the value of this essay. One might take this to mean that we should avoid hard problems, but we must believe that Dijkstra was not so simple as to suggest this. The point is that when building programs, we must choose an intellectually manageable approach, and reject the apparently easier approach of just starting to write code and seeing what happens. In order words, Dijkstra is telling us to make our software well organized, or not at all.

Big deal, one might say. But in my experience this is the single most common root of failure and near failure. It sounds simple - if you don't understand it, don't build it. Yet all too often, we start to build things with a superficial understanding of the problem, instead of taking the time to think through our solution a bit more.

Furthermore, Dijkstra provides some practical steps we can use (which correspond to one or more of his six arguments) in order to make sure what we're doing is intellectually manageable.

The first (arguments one, two, and three) is perhaps the most confusing and most powerful. Dijkstra urges us, when thinking of a high level design of a program, to start by thinking of how we would prove the program correct, and base our design on the structure of the proof. The confusion here is that Dijkstra was not referring to a "proof" in the way academic computer scientists understand "proof of correctness", nor to the way a high-school student understands a geometry proof, nor to something like test driven design (although all can be valuable, in the right context). Rather he was referring to "proof" the way a mathematician understands proof - the first step of which is a description of the problem in a way that clarifies the most relevant points. The most beautiful proofs in modern mathematics are treasured by mathematicians not because of their clever application of obscure logic, but because they provide a method of looking at a problem that makes the solution obvious.

This is what Dijkstra is promoting - finding an organizational structure for your software that makes it obvious what the code needs to do.

The discipline lies in not embarking on large projects until we have found this way of looking at things. It is admittedly very difficult, but also very important. In fact, I would argue that without this view of the problem, a project is doomed to failure or near failure. Discovering that we don't really understand the problem in the middle of a project can get very expensive very quickly, whereas spending the time in the beginning is much more cost effective. Its like sailing across the ocean - better to make your plans in port, than discover you forgot something halfway between San Francisco and Honolulu.


The second practical step Dijkstra proposes is one that we can use to help achieve this simplifying view (argument four). It is to use abstraction:

We all know that the only mental tool by means of which a very finite piece of reasoning can cover a myriad cases is called "abstraction"; as a result the effective exploitation of his powers of abstraction must be regarded as one of the most vital activities of a competent programmer. In this connection it might be worth-while to point out that the purpose of abstracting is not to be vague, but to create a new semantic level in which one can be absolutely precise. - EWD

When I first started programming, I worked on a project that had its own implementation of a hash table. We had to worry about hit rates, hash collisions, and so on, and could only work on strings! Now, whether you're writing in Java and using a HashMap, or in Perl and using associative arrays (aka hashes), or any other language, a perfectly reliable hash table is available for free, works simply and reliably, and for most data types. Likewise we think nothing of writing code which adds an integer value to a floating point value - yet this too was once a headache.

And the key point of an abstraction here is to find ways that we can use A and B in the same way, thus freeing us from the intellectual work of keeping them distinct - like adding a float to an int. In a shopping cart we might define a group of things that are "line items", all of which can have a price, a discount, a tax charge, and so on. Whether the thing is shipping or a widget, if we can treat it as a "line item", we will have made calculating and re-calculating the total much easier.


Argument five is our third practical step - using a good programming language. This is a very loaded subject, and many reasonable people feel it has been crushed beneath the weight of the ranting terabytes already written about it. But Dijkstra, as usual, has something quite profound to say about this:

Finally, in one respect one hopes that tomorrow's programming languages will differ greatly from what we are used to now: to a much greater extent than hitherto they should invite us to reflect in the structure of what we write down all abstractions needed to cope conceptually with the complexity of what we are designing. - EWD

This is, when it comes down to it, the strongest argument in favor or against a language - does it clearly reflect the structure of the idea behind the program, or does it obscure the structure. Almost all modern languages (C and its descendants, Java, Perl, Python, Ruby, and so on) can be used to clearly reflect the structure of the problem, and all are much superior to now out-dated languages such a BASIC, or Cobol, etc. However, unskillful use of these same languages can also create great obscurity. Dijkstra describes at length how our choice of language affects our thinking, which is quite true - but I believe the languages we use today much more similar to each other than the choices he faced 30 years ago, and we are now struggling less with languages and more with design paradigms (and that's definitely another post).

Finally, the fourth step - make your structure hierarchical (his sixth argument).

I do not know of any other technology covering a ratio of 10¹⁰ or more: the computer, by virtue of its fantastic speed, seems to be the first to provide us with an environment where highly hierarchical artefacts are both possible and necessary. - EWD

This basically means to layer abstraction on abstraction. Actually, this is often described as a problem, and it can be a serious problem. Its like the architecture of a building - if the layers are complimentary and harmonious, the building is successful. If the layers are put together willy-nilly, the result is a rickety structure prone to collapse. This is really where craft, or skill, comes in, which is the theme of this blog. But for now we're just exploring the foundations. And Dijkstra's instruction is clear: carefully use layers to make our creation intellectually manageable.

This post has been longer than hope will be usual - and it has taken longer too. But this essay of Dijkstra's made quite an impression on me, and it has quite a lot of meat on it.
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Code Read 2 - Dijkstra on Goto

Edsger W. Dijkstra, a giant of computer science, wrote an article long ago arguing that the "goto" statement was bad for programmers and the programs they wrote. Week 2 of Code Reads covers this article.

The statement "goto is bad" is exactly the kind of attention getting statement that provokes internecine fights between partisans of various languages. Unfortunately, the flame-wars usually miss the most relevant points. I'm definitely in the "no silver bullet" school, in fact I'm in a sub-sect of that school that says "your choice of language in and of itself is almost irrelevant to the success of the project". Obviously, Logo would be an inappropriate choice of language for building a web site, and for parsing log files Perl is a lot easier than Java. But the chief benefits of one language or another are using the skills of the people available, fitting in with a larger organization, and the availability of tools and libraries suitable for the job, not the language constructs.

So if language constructs are less than relevant, what is the point of Dijkstra's article? I found Joel Neely's comments in the Code Reads discussion section particularly insightful: the problem with "goto" is that it breaks the metaphors we develop to organize our code.

Dijkstra himself makes this fairly clear:

"My first remark is that, although the programmer's activity ends when he has constructed a correct program, the process taking place under control of his program is the true subject matter of his activity, for it is this process that has to accomplish the desired effect; it is this process that in its dynamic behavior has to satisfy the desired specifications." - EWD

I take this to mean that code is not the end goal here - correct execution is the goal. Or to use modern language - the business logic must solve the business problem. That should be the focus of our activities, not the code itself.

"My second remark is that our intellectual powers are rather geared to master static relations and that our powers to visualize processes evolving in time are relatively poorly developed. For that reason we should do (as wise programmers aware of our limitations) our utmost to shorten the conceptual gap between the static program and the dynamic process, to make the correspondence between the program (spread out in text space) and the process (spread out in time) as trivial as possible." - EWD

Although Dijkstra is saying a lot more than just this, the key point here is that we should make sure that the way we build a program bears a simple correspondence to the way it works, and more specifically, to a way we can think about it.

Which brings us back to the chief problem with "goto" statements - they tend to obscure the underlying logic of the program, instead of making it more apparent. They may make writing code marginally easer but that make building software much more difficult.
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