Pie-Decoration with Python

Some while ago, I found out that it’s actually quite easy to write your own decorators in Python. That thing that is called a “pie” syntax, available since Python 2.4 but still is mostly only the stuff of some frameworks like Django, Flask or PyTango. As to the “what” and especially “why??”, one might benefit from some thoughts I recently verified.

Motivation: As several of our software projects help our customers in supporting their experimental research with Supervistory Control and Data Acquisition (SCADA) applications, we have build a considerable knowledge base around the development with the open-source Tango Controls system. For me as a developer, its Python implementation PyTango makes my life significantly easier, because I can sketch out Tango applications, like Tango Device Servers, clients for data analysis, plotting live data etc. with little to none overhead. Less than an hour of development time usually gets you started.

PyTango actually makes it that easy to code the basic functionality of a device in a network structure with all the easy Tango features – well, you have to set up Tango once. But then the programming becomes easy. E.g. a current measurement device which is accessible from anywhere in your network could basically only need:

class PowerSupply(Device):
 
    def init_device(self):
        Device.init_device(self)
        self._current = 0
 
    @attribute(label="Current", unit="mA", dtype=float)
    def current(self):
        return self._current
 
    @current.write
    def current(self, current):
        self._current = current

Compare that to the standard C++ Tango implementation, where is all that would be loads of boilerplote code.

Now, this not unusual for Python. Hiding away the ugly implementation in its libraries or frameworks so you can focus on the content. However, you need to trust it, and depending on what kind of Python code you usually enjoy to read, this can make you think a bit. What is this usage of @ doing there? Isn’t this Java code??

But to the contrary: in Java, the @annotations are a way of basically interfering with the way the compiler itself behaves. For Python, the pie is pure syntactical sugar. In a way, they both address a similar way of your source code telling you “the next thing is treated in a specific way”, but whereas you would dig quite deep in Java to produce useful custom annotations (if you know otherwise, tell me), decorating pies in Python can easily help you to dynamically abstract layers of code away to places where it’s nicer and cleaner.

It turns out: A Python decorator is any function that maps a function to a function; i.e. it takes a function as an argument and returns the same or a different function. Easy enough; as in Python, functions are first-class objects. They can be passed around and extended accordingly.

But… Every programming pattern comes with the question: “What do I gain for learning such a new habit?”

Can and should you write your own decorators?

Under the hood, something like this happens. You define a decorator e.g. like

def my_decorator(func):
    print("the decorator is initialized")

    def whatever():
        print("the function is decorated")
        return func()

    return whatever

giving you instant access to your own decorator magic:

@my_decorator
def my_func():
    print("the decorated function is called")

A function call of my_func() now results in the output

the function is decorated
the decorated function is called

while the first “the decorator is initialized” in only executed at the declaration of the @my_decorator syntax itself.

This pie syntax is pure syntactical sugar. It does nothing more than if you instead had defined:

def my_anonymous_func():
    print("the decorated function is called")
my_func = my_decorator(my_anonymous_func)

But it appears somehow cleaner, avoiding the need of the two “my_anonymous_func” that are not useful anywhere else in your code. You stash away more irrelevant implementation details from the actualy meaning of “what is this method/function actually for?”. Now you can pack my_decorator in your own set utility functions as you would with any re-usable code block. To make the example more sophisticated, you can also process function arguments (*args, **kwargs) this way; or extend previously decorated functions with further functionality… and while the Decorator itself might be a bit more complex to read, you can test that separatly, and from then on, the actual __main__ code is tidy and easy to extend.

def my_decorator(func):
    # do setup stuff here

    def whatever(*args, **kwargs):
        print("The keyword argument par is:", kwargs.get('par', None))
        return func(*args, **kwargs)

    def whatever2(func2):
        def some_inner_function():
            print("Call the second function and do something with its result")

            # note that the _actual_ function call of the decorated function would happen in the very core of the decorating function
            return func2()
        return some_inner_function

    result = whatever
    result.other_thing = whatever2
    return result


if __name__ == '__main__':
    print("START")

    @my_decorator
    def my_func(*args, **kwargs):
        print("original my_func", kwargs.get('par', None))

    @my_func.other_thing
    def my_func2():
        pass

    my_func(par='Some keyword argument')
    my_func2()

So really, we are equipped to do anything. Any scenario, in which a function call should actually be guided by one or more extra actions, might be nicely packaged in a decorator. Which gives you a number of good use cases as e.g.

  • Logging (if only for debug reasons)
  • Additional metrics (e.g. performance evaluation)
  • Type checks (making even simple scripts more robust)
  • Error Handling
  • Registering of any service or entity e.g. in one centralized list structure
  • Updates on a user interface
  • Caching, e.g. to ease some expensive operation or asynchronous action
  • or any such meta-pattern that you find yourself repeating in otherwise unrelated scenarios.

And more than that, a good name choice of your decorator gives your code a nice self-explaining semantic structure. You describe more “what”, less “how” of a block of code.

I like that pattern, but I always thought the @ looks somewhat cryptical. If you have any objection, want to warn me about unforeseen implications or generally think this was always super-obvious, let me know 🙂

Who watches the FileSystemWatcher?

One of the ways we sometimes implement communication with legacy systems is via the file-system. The legacy system will write files about some events into a predefined directory, and the other system watches this directory for changes. In C#/.NET, the handy FileSystemWatcher class is a great tool for that.

We had a working solution using that in production for the last two years. Then it suddenly stopped working. There was no apparent change in the related code, so I suspect our upgrade from .NET Core 2.1 to .NET 5.0 triggered the change in behavior. The code looked something like this:

public void BeginWatching()
{
    var filter = NotifyFilters.LastAccess | NotifyFilters.LastWrite
        | NotifyFilters.FileName | NotifyFilters.DirectoryName;

    var watcher = new FileSystemWatcher
    {
        Path = directory,
        NotifyFilter = filter,
        Filter = "*.txt",
        EnableRaisingEvents = true,
    };
    /* Hook up some events here... */
}

And after some debugging, it turned out none of the attached event handlers were firing anymore. The solution was to not let go of the watcher instance, and keep it around in the enclosing class.

this.watcher = new FileSystemWatcher

This makes sense, of course. Before, the watcher was only a local variable, and could be collected by the garbage collector at any moment. That, in turn, disabled the process, causing no more events to be emitted.

Interestingly, a few days later, my student asked about his FileSystemWatcher also no longer working. I immediatly suspected the same problem, but when we looked at the code, he had already moved the watcher into a property of the enclosing class. Turns out, for him the problem was just one level up: the enclosing class was only created as a local variable, and the contained watcher stopped after that went out of scope.

Now the only question is: why did we never observe this before? Either something in the GC changed, or something in the implementation of the watcher changed. Can anyone enlighten the situation?

Applied User Research on my own pile of synthesizer machines

Last year, I moved. Moving into a new apartment is very much akin to a major rewrite of a complex piece of software. A piece of software with a limited amount of users, maybe (well, me, my girlfriend, that’s it), but with an immensely sophisticated structure of requirements… despite the decade-long experience of “living somewhere” one usually has at this point.

For example, I have a scarce habit of hoarding hardware synthesizers – from Soviet-era monstrosities like the Поливокс to modern machines, they have a few things in common, as they

  1. take quite some space (due to their extensive wiring) and some are heavy
  2. idle around for most of the time (I mean, I have a job)
  3. are versatile enough not to have a clear-cut function in any workflow.

These are somewhat essential. All in all, I had some unassigned space in my new home and my machines instantly colonized there. Like his original version of “work expands to fill the time available“, there seems to be another Parkinson‘s Law correlating hardware synthesizers and the space you allow them to have. So basically, they now occupied one room of their own.

Which could be the end of the story and everyone would live happily ever after. If you have, like, a Googol amount of rooms. And considering Point 2 above – this solution feels quite like a waste.

Now – also last year, I began to deep-dive into the techniques of User Experience. And basically, my problem is pretty much comparable to a customer with a few quite diverging requirements. Who wants his problem solved, but hasn‘t yet figured out his actual needs to begin with.

Ergo, I should be able to use my insights of the field of UX, or Interaction Design, directly to my advantage, by applying techniques of User Research to my own behaviour.

And the first question should always be: By which approach do we get the largest understanding by the least effort? But the zeroth question is actually: How “wicked” is my problem?. Do I have an absolutely ill-defined, ever-changing, non-testable set of challenges? Or is my problem-solving rather a technical feat, implementing the best patterns, clearest details, best documentation?

Indeed. Point 3 above makes my problem rather ill-defined. On some wickedness scale, with 1 being a quick YouTube search for a How-To, 10 being a problem that I would need to go on a week-long mountain retreat with daily meditation sessions… I would give it a 6-7.

This feels like it should be in the range of difficult, but solvable with a kind of generalized abstract thinking. I choose to opt for the technique of the Five Whys: The goal is to find a consecutive number of deeper questions after my problem solving. But generally, I understand this as

  • “Five” is a general number one can aim for. There can be more, less, and there can be branches in the questioning.
  • “Why” is a placeholder for any qualifier that goes to a more abstract level. It can also be a „What do you want…“, „How about…“, „What‘s wrong with…“ serving that purpose

So. I consider myself sitting on opposite sides of a table and asking:

  1. What do you want to accomplish, and why?
    • I want to have a truckload of synthesizers, fully functional, and also not to waste my space.
  2. Why do you need your space?
    • Not only do I also have other stuff. Less clutter is generally a way to improve life quality.
  3. Why don‘t you just get rid of the machines, i.e. selling, basement, …?
    • Well. I do want to have access to spontaneous synthesizer jams. The pandemic makes it hard to get that creative input anywhere else.
  4. Why does this need to be spontaneous?
    • Because musical, like any creative flow, comes spontaneously. I don‘t want to have a great idea gone by because of long efforts in setting up.
  5. Why would set up times have to be slow?
    • Because in an strictly ordered system I need to collect stuff from various spaces, i.e. the synthesizer itself, the power plug from a box of power plugs, cables for MIDI, audio, control voltages, …
  6. Why would these have to be in their ordered boxes, for apart from the synthesizer?
    • Hm. Well, I guess they wouldn‘t have to be. That‘s just what one would do..?

Now basically, this example did not happen as straightforward as I just made it seem, but it helped me to channel my focus on a rule that is actually quite known in the design of enjoyable user interfaces: „Group things according to their usage, not their nature“. This is a form of reducing cognitive load. UI designers sometimes make this mistake, e.g. grouping “everything that is a filter” in one section, “everything that is a configuration” in one section, and so on; focussing more on the technical implementation of what these are, not on the proximity in the actual domain. This gets worse, the more technical any domain in its essence is, which is the mistake I did.

Wiring hardware synthesizers together is a very technical task, but there is much more use in grouping what belongs together when one wants to use it, not when one looks at its definition.

So now I have it. I, as a user, am happy that I, as a researcher, actually asked stupid questions like “Why don‘t you sell all the garbage?” in order to channel my focus to a system, in which setting up the whole stuff is rather quick, reducing the cognitive load, or rather shift it to the cleanup process – which is fine because I now can trust the system 😉

Bridging Eons in Web Dev with Polyfills

Indeed, web development is kind of peculiar. On the one hand, there‘s seldom a field in which new technologies overturn each other at that pace, creating very exciting opportunities ranging from quickly sketching out proof-of-concepts to the efficient construction of real-world applications. On the other hand, there is this strange air of browser dependency and with any new technology one acquires, there‘s always the question of whether this is just some temporary fashion or here to stay.

Which is why it hapens, that one would like to quickly scaffold a web application on the base of React and its ecosystem, but has the requirement that the customer is – either voluntarily or forced by higher powers – using some legacy browser like Internet Explorer 11, for which Microsoft has recently announced its end of life support for 30th November this year. Which doesn’t sound nice for the… *searching quickly* … 5% of desktop/laptop users that still use this old horse, but then again, how long can you cling to an outdated thing?

For the daily life of a web developer, his mind full of peculiarities that the evolution of the ECMAScript standard which basically is JavaScript, there is the practical helper of caniuse.com, telling you for every item of your code you want to know about, which browser / device has support and which doesn’t.

But what about whole frameworks? When I recently had my quest for a IE11-comptabile React app, I already feared that at every corner, I needed to double-check all my doing, especially given that for the development itself, one is certainly advised to instead use one of the browsers that come with a quite some helpful developer tools, like extensions for React, Redux, etc. — but also the features in the built-in Console, where it makes your life a lot easier whether you can just log a certain state as a string of “[Object object]” or a fully interactive display of object properties. Sorry IE11, there are reasons why you have to go.

But actually, then, I figured, that my request is maybe not that far outside the range of rather widespread use cases. Thus, the chance that someone already tried to tackle the problem, aren’t so hopeless. And so this works pretty straightforward:

  • Install “react-app-polyfill”, e.g. via npm:
npm install react-app-polyfill
  • At the very top of your index.js, add for good measure:
import "react-app-polyfill/ie11";
import "react-app-polyfill/stable";
  • Include “IE 11” (with quotes) in your package.json under the “browserlist” as a new entry under “production” and “development”

That should do it. There are people on the internet that advise removing the “node_modules/.cache” directory when doing this in an existing project.

The term of a polyfill is actually derived from some kind of putty, which is actually a nice picture. It’s all about allowing a developer to use accustomed features while maintaining the actual production environment.

Another very useful polyfill in this undertaking was…

// install 
npm install --save-dev @babel/plugin-transform-arrow-functions

// then add to the "babel" > "plugins" config array:
"babel": {
    "plugins": [
      "@babel/plugin-transform-arrow-functions"
    ]
  }

… as I find the new-fashioned arrow function notation quite useful.

So, this seems to bridge (most of) the worries one encounters in this web dev world where use cases span eons of technology evolution. Now, do you know any more useful polyfills that make your life easier?

What is it with Software Development and all the clues to manage things?

As someone who started programming a long time ago (roughly 20 years, now that I think about it), but only in recent years entered the world of real software development, the mastery of day-to-day-challenges happens to consist of two main topics: First, inour rapidly evolving field we never run out of new technologies to learn, and then, there’s a certain engineering aspect underlying, how to do things in a certain manner, with lots of input every year.

So after I recently shared some of such ideas with my friends — I indeed still have a few ones of those), I wondered: How is it, that in the modern software development world, most of the information about managing things actually comes from the field itself, and rather feeding back its ideas of project management, quality, etc. into the non-software-subspaces of the world? (Ideas like the Agile movement, Software Craftmanship, the calls of doing things Lean and Clean, nowadays prospered so much that you see their application or modification in several other industries. Like advertisement, just as an example.)

I see a certain kind of brain food in this question. What tells software development apart from other current fields, so that there is a broad discussion and considerable input at its base level? After all, if you plan on becoming someone who builds houses, makes cars, or manages cities, you wouldn‘t engage in such a vivid culture of „how“ to do things, rather focussing on the „what“.

Of course, I might be mistaken in this view. But, by asking: what actually tells software development apart from these other fields of producing something, I see a certain kind of brain food, helpful for approaching every day tasks and valuing better tips over worse ones.

So, what can that be?

1. Quite peculiar is the low entry threshold in being able to call yourself a “programmer”. With the lots of resources you get at relatively little cost (assumption: you have a computer with a working internet connection), you have a lot of channels by which you can learn the „what“ of software development first, and saving the „how“ for later. If you plan on building a house, there‘s not a bazillion of books, tutorials, and videos, after all.

2. Similarly, there‘s the rather low cost of failure when drafting a quick hobby project. Not always will a piece of code that you write in your free time tell yourself „hey man, you ever thought about some better kind of architecture?“ – which is, why bad habits can stick and even feel right. If you choose the „wrong“ mindset, you don‘t always lose heaps of money, and neither do you, if you switch your strategy once in a while, you also don‘t automatically. (you probably will, though, if you are too careless in this process).

3. Furthermore, there‘s the dynamic extension of how your project is going to be used („Scope Creep“). One would build a skyscraper in a different way than a bungalow (I‘m not an expert, though), but with software, it often feels like adding a simple feature here, extending the scope there, unless you hit a point where all its interdependencies are in a complex state of conflict…

4. Then, it‘s a matter of transparency: If you sit in a badly designed car, it becomes rather obvious when it always exhausts clouds of black smoke. Or your house always smells like scents of fresh toilet. Of course, a well designed piece of software will come with a great user experience, but as you can see in many commercial products, there also is quite some presence of low-than-average-but-still-somehow-doing-what-it-should software. Probably users are more tolerant with software than with cars?

5. Also, as in most technical fields, it is not the case that „pure consultants“ are widely received in a positive light. For most nerds, you don‘t get a lot of credibility if you talk about best practices without having got your hands dirty over a longer period of time. Ergo, it needs some experienced software programmers in order to advise less experienced software programmers… but surely, it‘s questionable whether this is a good thing.

6. After all, the requirements for someone who develops a project might be very different in each field. From my academical past in computational Physics, I know that there is quite some demand for „quick & dirty“ solutions. Need to add some Dark Matter in your model here? Well, plug this formula in and check the results. Not every user has the budget or liberty in creating a solid structure of your program. If you want to have a new laboratory building, of course, you very well want it it do be designed as good as it can get.

All in all, these observations somehow boil down to the question, whether software development is to be seen more like a set of various engineering skills, rather like a handcraft, an art, or a complex program of study. It is the question, whether the “crack” in this field is the one who does complex arithmetics in its head, or the one who just gets what the customer wants. I like thinking about such peculiar modes of thought, as they help me in understanding what kinds of things I should learn next.

Or is there something completely else to it?

Compiling Agda 2.6.2 on Fedora 32

Agda is a dependently typed functional programming language that I like very much. Its latest versions have some special features which are not supported by any more well known languages, for example higher inductive types. Since I want to use all the special features of Agda, I regularly compile the latest version. This is a procedure which comes with a few surprises more often than not, so this post is about saving you the time it took me to figure out what to do.

I like to compile Agda using the Haskell tool Stack, which can be installed with

curl -sSL https://get.haskellstack.org/ | sh

The sources of Agda have to be checked out with all submodules – otherwise there will be some weird “cabal” (another Haskell tool, more basic than Stack) errors which I was not able to understand. This can be done with:

git clone --recurse-submodules https://github.com/agda/agda.git

Now if you go to the Agda folder

cd agda

There should be files called “stack-8.8.4.yaml” and similar. Those files can can tell Stack how to build Agda. The number is the version of the Haskell compiler which is used to build Agda. I usually use the latest, you do not have to figure out which (if any) is installed on your system, since Stack will just download the appropriate compiler for you.

However, just running stack failed for my on Fedora 32 due to some linking problem in the end. It turned out, that “libtinfo.so” was not found by the linker. “libtinfo.so.6” is available on Fedora 32, so adding a link to it fixed the problem:

sudo ln -s /usr/lib64/libtinfo.so.6 /usr/lib64/libtinfo.so

Now, you can tell Stack to get all necessary things and compile and install Agda with:

stack install --stack-yaml stack-8.8.4.yaml

This also installs a binary into “~/.local/bin” which is in PATH on Fedora 32 by default, so you should be able to call agda from the command line. Also, you can use “agda-mode” to configure emacs for agda.

Be precise, round twice

Recently after implementing a new feature in a software that outputs lots of floating point numbers, I realized that the last digits were off by one for about one in a hundred numbers. As you might suspect at this point, the culprit was floating point arithmetic. This post is about a solution, that turned out to surprisingly easy.

The code I was working on loads a couple of thousands numbers from a database, stores all the numbers as doubles, does some calculations with them and outputs some results rounded half-up to two decimal places. The new feature I had to implement involved adding constants to those numbers. For one value, 0.315, the constant in one of my test cases was 0.80. The original output was “0.32” and I expected to see “1.12” as the new rounded result, but what I saw instead was “1.11”.

What happened?

After the fact, nothing too surprising – I just hit decimals which do not have a finite representation as a binary floating point number. Let me explain, if you are not familiar with this phenomenon: 1/3 happens to be a fraction which does not have a finte representation as a decimal:

1/3=0.333333333333…

If a fraction has a finite representation or not, depends not only on the fraction, but also on the base of your numbersystem. And so it happens, that some innocent looking decimal like 0.8=4/5 has the following representation with base 2:

4/5=0.1100110011001100… (base 2)

So if you represent 4/5 as a double, it will turn out to be slightly less. In my example, both numbers, 0.315 and 0.8 do not have a finite binary representation and with those errors, their sum turns out to be slightly less than 1.115 which yields “1.11” after rounding. On a very rough count, in my case, this problem appeared for about one in a hundred numbers in the output.

What now?

The customer decided that the problem should be fixed, if it appears too often and it does not take to much time to fix it. When I started to think about some automated way to count the mistakes, I began to realize, that I actually have all the information I need to compute the correct output – I just had to round twice. Once say, at the fourth decimal place and a second time to the required second decimal place:

(new BigDecimal(0.8d+0.315d))
    .setScale(4, RoundingMode.HALF_UP)
    .setScale(2, RoundingMode.HALF_UP)

Which produces the desired result “1.12”.

If doubles are used, the errors explained above can only make a difference of about 10^{-15}, so as long as we just add a double to a number with a short decimal representation while staying in the same order of magnitude, we can reproduce the precise numbers from doubles by setting the scale (which amounts to rounding) of our double as a BigDecimal.

But of course, this can go wrong, if we use numbers, that do not have a short neat decimal representation like 0.315. In my case, I was lucky. First, I knew that all the input numbers have a precision of three decimal places. There are some calculations to be done with those numbers. But: All numbers are roughly in the same order of magnitude and there is only comparing, sorting, filtering and the only honest calculation is taking arithmetic means. And the latter only means I had to increase the scale from 4 to 8 to never see any error again.

So, this solution might look a bit sketchy, but in the end it solves the problem with the limited time budget, since the only change happens in the output function. And it can also be a valid first step of a migration to numbers with managed precision.

Math development practices

As a mathematician that recently switched to almost full-time software developing, I often compare the two fields. During the last years of my mathematics career I was in the rather unique position of doing both at once – developing software of some sort and research in pure mathematics. This is due to a quite new mathematical discipline called Homotopy Type Theory, which uses a different foundation as the mathematics you might have learned at a university. While it has been a possibility for quite some time to check formalized mathematics using computers, the usual way to do this entails a crazy amount of work if you want to use it for recent mathematics. By some lucky coincidences this was different for my area of work and I was able to write down my math research notes in the functional language Agda and have them checked for correctness.

As a disclaimer, I should mention that what I mean with “math” in this post, is very far from applied mathematics and very little of the kind of math I talk about is implement in computer algebra systems. So this post is about looking at pure, abstract math, as if it were a software project. Of course, this comparison is a bit off from the start, since there is no compiler for the math written in articles, but it is a common believe, that it should always be possible to translate correct math to a common foundation like the Zermelo Fraenkel Set Theory and that’s at least something we can type check with software (e.g. isabelle).

Refactoring is not well supported in math

In mathematics, you want to refactor what you write from time to time pretty much the same way and for the same reasons as you would while developing software. The problem is, you do not have tools which tell you immediately if your change introduces bugs, like automated tests and compilers checking your types.

Most of the time, this does not cause problems, judging from my experiences with refactoring software, most of the time a refactoring breaks something detected by a test or the compiler, it is just about adjusting some details. And, in fact, I would conjecture that almost all math articles have exactly those kind of errors – which is no problem at all, since the mathematicians reading those articles can fix them or won’t even notice.

As with refactoring in software development, what does matter are the rare cases where it is crucial that some easy to overlook details need to match exactly. And this is a real issue in math – sometimes a statements gets reformulated while proving it and the changes are so subtle that you do not even realize you have to check if what you prove still matches your original problem. The lack of tools that help you to catch those bugs is something that could really help math – but it has to be formalized to have tools like that and that’s not feasible so far for most math.

Retrospectively, being able to refactor my math research was the biggest advantage of having fully formal research notes in Agda. There is no powerful IDE like they are used in mainstream software development, just a good emacs-mode. But being able to make a change and check afterwards if things still compile, was already enough to enable me to do things I would not have done in pen and paper math.

Not being able to refactor might also be the root cause of other problems in math. One wich would be really horrible for a software project, is that sometimes important articles do not contain working versions of the theorems used in some field of study and you essentially need to find some expert in the field to tell you things like that. So in software project, that would mean, you have to find someone who allegedly made the code base run some time in the past by applying lots of patches which are not in the repository and wich he hopefully is still able to find.

The point I wanted to make so far is: In some respects, this comparison looks pretty bad for math and it becomes surprising that it works in spite of these deficiencies. So the remainder of this post is about the things on the upside, that make math check out almost all the time.

Math spent person-centuries on designing its datatypes

This might be exaggerated, but it is probably not that far off. When I started studying math, one of my lecturers said “inventing good definitions is not less important as proving new results”. Today, I could not agree more, immense work went into the definitions in pure math and they allowed me to solve problems I would be too dumb to even think about otherwise. One analogue in programming is finding the ‘correct’ datatypes, which, if achieved can make your algorithms a lot easier. Another analogue is using good libraries.

Math certainly reaps a great benefit from its well-thought-through definitions, but I must also admit, that the comparison is pretty unfair, since pure mathematicians usually take the freedom to chose nice things to reason about. But this is a point to consider when analysing why math still works, even if some of its practices should doom a software project.

I chose to speak about ‘datatypes’ instead of, say ‘interfaces’, since I think that mathematics does not make that much use of polymorhpism like I learned it in school around 2000. Instead, I think, in this respect mathematical practice is more in line with a data-oriented approach (as we saw last week here on this blog), in math, if you want your X to behave like a Y, you usually give a map, that turns your X into a Y, and then you use Y.

All code is reviewed

Obviously like everywhere in science, there is a peer-review processs if you want to publish an article. But there are actually more instances of things that can be called a review of your math research. Possibly surprising to outsiders, mathematicians talk a lot about their ideas to each other and these kind of talks can be even closer to code reviews than the actual peer reviews. This might also be comparable to pair programming. Also, these review processes are used to determine success in math. Or, more to the point, your math only counts if you managed to communicate your ideas successfully and convince your audience that they work.

So having the same processes in software development would mean that you have to explain your code to your customer, which would be a software developer as yourself, and he would pay you for every convincing implementaion idea. While there is a lot of nonsense in that thought, please note that in a world like that, you cannot get payed for a working 300-line block code function that nobody understands. On the other hand, you could get payed for understanding the problem your software is supposed to solve even if your code fails to compile. And in total, the interesting things here for me is, that this shift in incentives and emphasis on practices that force you to understand your code by communicating it to others can save a very large project with some quite bad circumstances.

Getting started with exact arithmetic and F#

In this blog post, I claimed that some exact arithmetic beyond rational numbers can be implemented on a computer. Today I want to show you how that might be done by showing you the beginning of my implementation. I chose F# for the task, since I have been waiting for an opportunity to check it out anyway. So this post is a more practical (first) follow up on the more theoretic one linked above with some of my F# developing experiences on the side.

F# turned out to be mostly pleasant to use, the only annoying thing that happened to me along the way was some weirdness of F# or of the otherwise very helpful IDE Rider: F# seems to need a compilation order of the source code files and I only found out by acts of desperation that this order is supposed to be controlled by drag & drop:

The code I want to (partially) explain is available on github:

https://github.com/felixwellen/ExactArithmetic

I will link to the current commit, when I discuss specifc sections below.

Prerequesite: Rational numbers and Polynomials

As explained in the ‘theory post’, polynomials will be the basic ingredient to cook more exact numbers from the rationals. The rationals themselves can be built from ‘BigInteger’s (source). The basic arithmetic operations follow the rules commonly tought in schools (here is addition):

static member (+) (l: Rational, r: Rational) =
    Rational(l.up * r.down + r.up * l.down,
             l.down * r.down)

‘up’ and ‘down’ are ‘BigInteger’s representing the nominator and denominator of the rational number. ‘-‘, ‘*’ and ‘/’ are defined in the same style and extended to polynomials with rational coefficients (source).

There are two things important for this post, that polynomials have and rationals do not have: Degrees and remainders. The degree of a polynomial is just the number of its coefficients minus one, unless it is constant zero. The zero-polynomial has degree -1 in my code, but that specific value is not too important – it just needs to be smaller than all the other degrees.

Remainders are a bit more work to calculate. For two polynomials P and Q where Q is not zero, there is always a unique polynomial R that has a smaller degree such that:

P = Q * D + R

For some polynomial D (the algorithm is here).

Numberfields and examples

The ingredients are put together in the type ‘NumberField’ which is the name used in algebra, so it is precisely what is described here. Yet it is far from obvious that this is the ‘same’ things as in my example code.

One source of confusion of this approach to exact arithmetic is that we do not know which solution of a polynomial equation we are using. In the example with the square root, the solutions only differ in the sign, but things can get more complicated. This ambiguity is also the reason that you will not find a function in my code, that approximates the elements of a numberfield by a decimal number. In order to do that, we would have to choose a particular solution first.

Now, in the form of unit tests unit tests, we can look at a very basic example of a number field: The one from the theory-post containing a solution of the equation X²=2:

let TwoAsPolynomial = Polynomial([|Rational(2,1)|])
let ModulusForSquareRootOfTwo = 
     Polynomial.Power(Polynomial.X,2) - TwoAsPolynomial
let E = NumberField(ModulusForSquareRootOfTwo)   
let TwoAsNumberFieldElement = NumberFieldElement(E, TwoAsPolynomial)

[<Fact>]
let ``the abstract solution is a solution of the given equation``() =
    let e = E.Solution in  (* e is a solution of the equation 'X^2-2=0' *)
    Assert.Equal(E.Zero, e * e - TwoAsNumberFieldElement)

There are applications of these numbers which have no obvious relation to square roots. For example, there are numberfields containing roots of unity, which would allow us to calculate with rotations in the plane by rational fraction of a full rotation. This might be the topic of a follow up post…

Some strings are more equal before your Oracle database

When working with customer code based on ADO.net, I was surprised by the following error message:

The german message just tells us that some UpdateCommand had an effect on “0” instead of the expected “1” rows of a DataTable. This happened on writing some changes to a table using an OracleDataAdapter. What really surprised me at this point was that there certainly was no other thread writing to the database during my update attempt. Even more confusing was, that my method of changing DataTables and using the OracleDataAdapter to write changes had worked pretty well so far.

In this case, the title “DBConcurrencyExceptionturned out to be quite misleading. The text message was absolutely correct, though.

The explanation

The UpdateCommand is a prepared statement generated by the OracleDataAdapter. It may be used to write the changes a DataTable keeps track of to a database. To update a row, the UpdateCommand identifies the row with a WHERE-clause that matches all original values of the row and writes the updates to the row. So if we have a table with two rows, a primary id and a number, the update statement would essentially look like this:

UPDATE EXAMPLE_TABLE
  SET ROW_ID =:current_ROW_ID, 
      NUMBER_COLUMN =:current_NUMBER_COLUMN
WHERE
      ROW_ID =:old_ROW_ID 
  AND NUMBER_COLUMN =:old_NUMBER_COLUMN

In my case, the problem turned out to be caused by string-valued columns and was due to some oracle-weirdness that was already discussed on this blog (https://schneide.blog/2010/07/12/an-oracle-story-null-empty-or-what/): On writing, empty strings (more precisely: empty VARCHAR2s) are transformed to a DBNull. Note however, that the following are not equivalent:

WHERE TEXT_COLUMN = ''
WHERE TEXT_COLUMN is null

The first will just never match… (at least with Oracle 11g). So saying that null and empty strings are the same would not be an accurate description.

The WHERE-clause of the generated UpdateCommands look more complicated for (nullable) columns of type VARCHAR2. But instead of trying to understand the generated code, I just guessed that the problem was a bug or inconsistency in the OracleDataAdapter that caused the exception. And in fact, it turned out that the problem occured whenever I tried to write an empty string to a column that was DBNull before. Which would explain the message of the DBConcurrencyException, since the DataTable thinks there is a difference between empty strings and DBNulls but due to the conversion there will be no difference when the corrensponding row is updated. So once understood, the problem was easily fixed by transforming all empty strings to null prior to invoking the UpdateCommand.