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On object-oriented programming

[written at the end of 2013 AD, during the Dark Ages of programming]

The programmer’s world is full of fads and superstitions. Every now and then there will be somebody who come up and announce: “I can save the world!” No matter how bad the ideas are, there will always be followers, and the ideas soon become their religion. They then develop their community or camp, try to let those ideas dominate the world, and try to make the ideas live forever.

Object-oriented programming (OOP) is such a religion. It claimed to be able to save the world from the so-called “software crisis”, but as a hindsight after so many years since it was introduced, not only didn’t OOP save us, it brought us way more confusion and harm than benefits. Unfortunately its dogmas and mispractices have become so wide-spread and deeply intrenched. In this article, I hope to provide my viewpoint into this matter and try to find out the lessons that we can learn.

Like every article on my blog, the opinions are completely personal and not representing my employers or professors.

Is everything an object?

“Everything is an object” is the core dogma of OOP and deemed as the highest standards of OO language design. Now let’s take a careful look to see if it is true, or if it is a good idea to make things that way.

Many people take “everything is an object” for granted because when this sentence is taken literally it matches their everyday experience. Since the word “object” in English basically means “a thing”, how can “everything is an object” be not true? But be careful since the definition of an “object” in OOP has a specific meaning which is very different from its meaning in English.

OOP’s definition of an object is “a combination of data fields and associated procedures known as methods“. Can you really fit everything into this model?

First let’s look at the real world and see if this definition can capture everything. Cars, trees, animals may sometimes be thought of as objects, but what about a change of the objects’ position, its velocity and duration? What methods do they have? Well, you may define classes called Velocity or Time, with methods such as addition, but do velocity and time really contain the things that you call “methods”? They don’t. They are just your imagination. You can add the velocities or time, but how can velocities or time contain the addition procedure? This is like saying that the bullets contain the gun.

So the most you can say is that “everything is an object” is a good way of thinking, but that is not true either. The definition of an object implies that a method can only belong to one object, but most of the time it doesn’t make sense thinking of it as belonging to any object. Say we have the expression 1+2, does the operator ‘+’ belong to 1, or does it belong to 2? You have to make some arbitrary choice. Since you can make a choice, this means that the ‘+’ operator doesn’t really belong to either of them. The operation is inherently outside of the objects.

So thinking of some things as objects may be helpful, but thinking of everything as an object is neither true nor useful. Unfortunately “everything is an object” has been taken as a dogma and the highest standard of OO language design. Some OO languages claim that everything is an object in them. Whenever you notice that something is not an object, somebody will try to make it one. They may succeed in that, but things get very complicated that way, because that’s not how things work.

The idealism of “everything is an object” is similar to “everything is a function” in the functional programming world and “everything is a set” in the math world. Before computer science was conceived there was a thing called the lambda calculus. Some people encoded everything including numbers and their operations, various data structures and control structures, … all in lambdas. One of the encodings of numbers is called the Church numeral. Every programming language researcher has played with them during their education. But unlike “everything is an object”, “everything is a function” has never become a dogma or marketing phrase. Those formulations sometimes provide thought experiments and inspirations to the researchers but nobody really use them for actual computation, because they are inefficient and they are not really how things work. They are just approximations (models) to some essence of computation that we can’t see. If you really use them for practical projects, things become complicated.

Mathematicians have a similar concept: set theory. Some geniuses encoded everything — numbers, operations on numbers, mathematical structures, … all in sets. Everything is just sets containing sets containing sets and so on. What’s the problem? But when they really tried to do their proofs using those sets, the proofs fell under their own weights. They are too complicated. Even with the complexity, set theory is not expressive enough to capture whatever the mathematicians have to say. Many people tried to fix it, but they all failed.

So “everything is an object” is in some sense on the same track of “everything is a function” and “everything is a set”. Good thought exercise, but doesn’t really work well in practice. I don’t think that there is some “one true language”. When compared to the “absolute truth” every theory is wrong, but some theories are more wrong than others. The model of OOP is too far from correct or practical. It’s somewhat like the flat earth theory. Until today some people still believe that the earth is flat and make all kinds of theories to prove it. Some of their arguments look very scientific, but do you believe in their formulas or a picture of the earth from a spaceship? When you get the fundamental things wrong and don’t throw them away, you have to patch them endlessly with even more complicated theories. You will have to make theories that bend the light and gravity in weird ways. And that’s what happened to OOP.

Are functions objects?

From what I know, the original motivation of putting functions inside objects was to support GUI applications. You click on a button and some function (a callback) will be invoked. For the convenience of referring to the button, the callback takes the triggered object as its first argument. Since the callback does nothing more than this, it seems to be convenient to just store it inside the button. And thus we had an “object” which combines the attributes of the button and a method (the callback). Indeed this is a good idea, but this limited usage case can’t really justify a universal notion of “everything is an object”, just like a two-mile walk can’t prove that the earth is flat.

If you really understand what is abstraction, you may have noticed that even the above story contains a subtle mistake: the callback in the button is not really a method. The true purpose of a method is to provide abstraction to the attributes, but the callback’s purpose is not to provide abstraction. It is just a usual function triggered by the button, which happens to take the button as its first argument.

Very few functions should be considered methods of an object. If you look carefully, most of the time the objects just serve as a namespace (or module) in which you can store attributes and functions, but those functions don’t logically belong to the objects. They just take the objects as inputs and produce some output. Only the functions that are most intimately connected to the attributes and provide an abstraction layer to them should be considered methods. Most of those are called “getters” or “setters”. Some others hide implementation details for more complex data structures such as lists, hash tables, sets etc.

In some languages such as Scala or Python, functions are also treated as objects, but they actually just wrapped the functions into an object, give them names such as “apply” or “call“, so that when the objects are “invoked” you know which functions to call. But putting a function into an object doesn’t really mean that functions are also objects, just like inviting friends to your house doesn’t make them your family.

Functions are fundamental constructs. They don’t belong to objects. They describe a change, transition or transformation of objects. They are not objects and can’t be simulated by objects. They are like a base case of an inductive definition. They are where the illusion of “everything is an object” ends.

The cost of excessive abstraction

The major appeal of OOP is abstraction (and thus code reusing and DRY), but actually most of those abstraction facilities are already provided by traditional procedural languages and functional languages. Some of them do it even better than OO languages. OO claims its originality by emphasizing abstraction much more strongly than other languages. The result is that OO programmers usually overdo it. Some of them pursue abstraction and code reusing to the degree as if they are everything about programming.

For the purpose of code reusing, OO encourages a level of abstraction which makes programs hard to understand and hard to analyze. I often see Java programs with multiple levels of inheritance, overloading and design patterns, but actually doing very little. And because there is so much code that doesn’t do useful things, it is really hard to find out which part of the code is doing the thing you want. It is like going through a maze. Another nice word for this is “robustness”. If I have to go into all this trouble to make code reusable or robust, I’d rather just make copies of the code and modify them, but keep each copy simple and easy to understand.

Whenever you criticize Java or C++ for their verbosity, OO proponents will tell you that they are not authentic OO languages. They would ask you to look at Smalltalk. If Smalltalk’s ways are that good, why almost nobody is using Smalltalk now? Because there are real problems in its approach. I think Smalltalk is the origin of over-abstraction and over-complication you find in other OO languages.

The “authentic” OO style of Smalltalk promotes the notion of “extremely late binding”, which basically means that the meaning of the program constructs is determined as late as possible. Late binding gives you a chance to swap out the underlying implementation without forcing the upper levels to change, but this also means that you are no longer sure what a piece of code means. When I look at expressions such as ‘1+2’ and ‘if (t) then … else …’ in Java or C++, I at least know for sure that they mean an integer addition and an usual conditional. But I’m no longer sure about this in an “extremely late binding language”, because the meaning of ‘+’ and ‘if” can be redefined. Giving the programmers the power of defining control structures is a bad idea, because soon your language will be abundant of quirky control structures designed by programmers who try to be clever. It will no longer be the language that you used to know.

An example for this feature is Smalltalk’s conditional structure, which looks like this:

result := a > b
    ifTrue:[ 'greater' ]
    ifFalse:[ 'less or equal' ]

You send a message ifTrue: to a Boolean object, passing as an argument a block of code to be executed if and only if the Boolean receiver is true.

First of all, if you really have a well-designed language, you shouldn’t be wanting to define your own control structures. As a seasoned Lisp/Scheme programmer, I have seen many custom-designed control structures (such as the various looping macros) over the years, but none of them turned out to be good ideas. I’d rather write slightly longer and more verbose code in the vanilla language than to learn those weird control structures. Second, if you are really genius enough to have invented another good control structure, the late binding feature of Smalltalk probably won’t provide you the necessary power for defining it. The power of functions as an abstraction tool is limited. It is strictly less powerful than Lisp/Scheme’s macros. Third, this feature of Smalltalk is not really a novel approach, and it has a serious problem. A similar but more beautiful conditional construct had been defined in lambda calculus since before computer science was born:

TRUE = λx.λy.x
FALSE = λx.λy.y
IF = λb.λt.λf.b t f

This is very beautiful and can be done in any functional language, but why none of the functional languages implement conditionals this way? Because when you see an expression IF b t f, you will have no idea whether it is a conditional or not, because IF can be redefined in the program. Also because IF is just a function, it may also accept unexpected values other than TRUE or FALSE. This may happen to make the conditional construct work but cause trouble later on. This is called “unintentional semantics”. This kind of bug can be very hard to track down.

This approach also makes compiler and static analysis hard. When the compiler sees IF b t f, it no longer knows that it is a conditional so it can’t optimize it that way. It has to treat it as a usual function call. Similarly when the type checker sees it, it doesn’t know what type to expect for b, because it may not be a conditional at all. The above argument against the lambda calculus can easily be adapted to Smalltalk.

So abstraction is a powerful weapon when used moderately, but when you do it in excess, it backfires. Not only does it make it hard for humans to understand the code, it makes automated analysis tools and compiler optimizations difficult or impossible to make.

Design patterns, the brain eater

Although OO languages are touted for their abstraction capabilities, they are actually not strong in terms of abstraction and expressiveness. There are certain things that are very easy to do in traditional procedural languages and functional languages, but has been made unnecessarily hard in OO languages. This is why design patterns appeared. Design patterns’ origin was mostly due to the dogma of “everything is an object”, the lack of high-order functions (or the correct implementation of them) and OO’s tendency of mystifying things.

When I first heard about design patterns I was already a PhD student at Cornell doing some PL research. I mostly used Standard ML and Haskell. After hearing my friends’ high opinions of the Design Patterns book (the “GoF” book) I developed curiosity, so I borrowed one from the library. Within a few hours I found a mapping from all the weird names it introduced to the programming techniques I had been using all the time. Some of them are so fundamental and they exist in every high-level language, so they don’t really need names. Most of the advanced ones (such as visitor) are transcriptions of functional programming concepts into a convoluted form in order to get around OO language’s limitations. Later on I found that Peter Norvig gave a talk on design patterns as early as 1998, pointing out that almost all of the design patterns will be “transparent” once you have first-class functions. This confirmed my observations — I don’t need them.

I have to admit that some of the design patterns are cleverly designed and contain some ingenuity. You really need to get to the essence of the OO languages’ internal magics and also understand lots of functional programming techniques in order to create them. But intelligence =/= wisdom. Even if they can achieve what functional languages can do, they are usually a lot more complicated. Choosing the hard ways can’t really prove your genius. When you have first-class functions, things become so much easier and you won’t even notice the design patterns’ existence. Like Peter Norvig said, they will become “transparent”. So what a good language designer should do is to add first-class functions into the language instead of proposing design patterns as workarounds.

Every time I remove a design pattern (some other people wrote), the code becomes simpler and more manageable. I just removed the last visitor pattern from my Java code a few days ago and I felt so relieved. They gave me nothing but extra work when they existed. They hindered my progress. By deeply understanding how OO languages are implemented, you can write more advanced things than those provided by design patterns but without actually using them. I owe these insights to some functional programming people. If you really want to understand the essence of OO design patterns and how NOT to use them, this little book may be a good starting point.

Unfortunately design patterns somehow got really popular in companies, to the degree of unbearable. I saw the GoF book on almost every bookshelf when I interned at Google. Even if you don’t write them yourself, there was almost no way you could avoid other people slipping design patterns into your code. Design patterns’ marketing strategy was much like weight loss products: “It can burn your fat without you doing any work!” They appeal to some new programmers’ hope that they can write programs without understanding the fundamental concepts of computer science. Just by applying several patterns and patching things together, they hope to have a good program. This is too good to be true. You end up doing more work than you hoped to avoid. Design patterns eat programmers’ brains. After using design patterns for some time, they no longer see things or write programs in clear and straightforward ways.

What is an OO language any way?

To this point we haven’t yet talked about what makes a language an “OO language” and what makes it not. Is it an OO language just because I can put both data fields and functions into a record? Or is it an OO language only if it also provides extremely late binding? How about inheritance, overloading, etc etc? Must I have all of them? Any of them?

It turns out that there is no good answer to this question. There really is no such thing as an “object-oriented language”. Objects can be part of a language, but it is just a small part of it. You can’t really say that a language is object-oriented just because it provides objects as a feature. The so-called OO languages are solidly rooted in traditional procedural programming (PP). OOP basically stole everything from PP, renamed the terminologies and acted as if the ideas were its own.

Historically the term OO was mainly used for marketing reasons. It could give a language some advantages of attracting people if you claim it to be an OO language, but now this advantage is diminishing because more and more people have realized the problems of OO’s methodology.

Harm in education and industry

Although OO has lots of problems, it is very successful in marketing and has risen to a dominant position over the years. Under social and market pressure, many colleges started using OO languages such as Java as their introductory language, replacing traditional procedural languages such as Pascal and functional languages such as Scheme. This in a large degree caused the students’ failure to learn the most essential concepts of programming. The only thing that OO emphasizes is code reusing, but how can you teach it to the students who can’t even write usable code, not to mention that code reusing is not really as important as some people believe.

At both Cornell and Indiana, I have been teaching assistant for introductory programming courses in Java. I still remember how confused the students were. Most of them had trouble understanding things such as the meaning of “this”, why everything needs to be put inside classes, why make every field private and use getters, the difference between a method and a static method, etc etc.

There is a good reason that they don’t understand — because OO is not how things work. Most of the time I feel that I was teaching design flaws and dogmas to them. Many of them learned very little in the end. Worse, some of those students really believed in OO. They ended up being proud of writing over-engineered and convoluted code. They no longer see things or write programs in straightforward ways. This is sad. I feel that we are no longer educating students as creative and critical thinkers, but mindless assembly line workers.

In industry, OO hasn’t really proved its effectiveness with evidence. Good systems may be built in a “OO language”, but the code is often written by people who understand the problems of OO and don’t embrace “everything is an object” or “design patterns”. Good programmers usually use workarounds in OO languages and are essentially writing in a traditional procedural style combined with bits from functional programming. So some OO languages and their tools may be pretty widely used, but the OO style doesn’t really have much influence on the advancements of programming as a field.

Final word

So what does this post has to say? A jihad against OO languages? Advocate functional programming? Neither. As I said, there is no such thing as an “OO language”, so where is the war? Every so-called OO language also contains good elements that it borrowed (or stole) from procedural languages or sometimes functional languages, so they are not completely useless.

It is the extra features added by OO in addition to procedural programming that are causing most of the problems. Those extra “true OO techniques” contain way more confusion than real value. In my experience, accepting even one or two of those ideas may put you into a series of troubles and wrong ways of thinking which may take a long time to examine and recover. They are like diseases.

Thus I suggest not to buy OO’s way of thinking and don’t try to exploit its “features”. By eschewing those problematic features you can still produce acceptable programs in an OO language, because you are essentially using it as an non-OO procedural language.

(Chinese translation by ZoomQuiet)

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Posted by on December 24, 2013 in oop, programming languages

 

Purely functional languages and monads

In general, functional languages are pleasant to work with because they support first-class functions, which are a very powerful modeling tool. But if you pursue the extreme — to use a purely functional language, you get adverse effects similar to OO design patterns. In a conventional OO language, having to use OO design patterns makes hard things even harder; but in a purely functional language, having to use pure functions to model side-effects makes trivial things hard and hard things impossible. So speaking of the two evils, OOP is the lesser one because at least easy things are still easy in them.

The problem with pure FP is: there exists things that are not pure.

Side-effects are real

Electrical engineers probably have the best understanding of purely functional languages, because electric wires are pure by default (if you are not paranoid enough to count heat as a side-effect). Purely functional languages are the analogous of combinational logic circuits. They are very useful and are an important part of a system, but you can’t use them alone to build up complex systems. This is why people invented flip-flops and sequential logic circuits. If you look at the design of the flip-flops, you will start to appreciate the ingenuity in them. They create memory out of “pure circuits”. And the memory is where the side-effects come from.

So pureness comes for free, but side-effects took efforts to invent. Unfortunately a large portion of the physical capabilities provided by the sequential circuits are disregarded by purely functional languages. Instead, purely functional languages are obsessed in simulating the effects on their own. There is a difference between the physical and the simulated. The simulated can’t be as efficient as the physical.

For a simple example, many efficient data structures rely on mutations to create connections between their components (think about circular data structures and networks). In such structures, side-effects act very much like a physical force to hold the parts together, and update them as needed. To implement this in a purely functional language, you have to use indirect ways. Every time you change it, you need to create a new data structure which shares most of the old data structure. But then you got into the trouble of keeping track of where the “current structure” is. It is moving in the dataflow and you have to pass it on. Had you used side-effects, the structure can stay at the same location, so you won’t need to worry that you will lose track of it. You don’t need to pass it on. This will save lots of administrative code.

Also sharing the old structures induces extra levels of indirection in the data structure, which causes significant overhead. Thus purely functional data structures can’t really match the performance provided by its impure counterpart. Purely functional data structures also cause lots of object creation and thus stress the garbage collector.

Some people say that purely functional data structures will reduce contention when there is lots of concurrency, but notice that if the observers of the old data structure “purely update” it, they will hold a different structure other than it’s current state. After that point, the universe is “forked” and they will live in completely different worlds. You will lose consistency. If you really want all threads to see the same data structure, then the contention is unavoidable, because you need a channel for the information to pass through. Nothing can save you from the contention because there is data dependency.

Everything is persistent in purely functional data structures, but how often do you need the outdated ones? In impure data structures, you still have the choice of making copies when necessary and achieve the same persistence effect, just with better performance.

Monads are design patterns

Purely functional languages also complicates the programs and ensue a huge cognitive cost. Modeling side-effects using pure functions is in the same mentality of wrapping functions inside objects as in OOP. They are both over-engineering and cause unnecessary manual labor.

One of the major “design patterns” in purely functional languages is called “monads”, a highly stylized way of structuring side-effects. If you look deep into them, monads make programs complicated and hard to write, and monad transformers are in essence a hack to get around monads’ limitations — they are not principled ways of composing monads. Representing side-effects using monads is as convoluted as writing interpreters or compilers using visitor patterns. For this matter, I wrote a short article some time ago which not many people have read:

To write programs in a purely functional programming language is much like living in a wired world. In such a world, there are no electromagnetic waves nor sound waves, so you don’t have wifi, cell phones, satellite TV, radios, etc. You don’t even have light or sound. In other words, everything is blind and deaf.

All information must pass through wires or pipes, connected by switch boxes which we call “monads”. You must carefully route all the wires and pipes and connect them correctly before any information processing device, including your eyes and ears, can properly work.

Trivial things in other languages (such as random number generators or circular data structures) become non-trivial in a purely functional language. Easy things often become research problems when you try to write them using monads, so you often see papers titled similar to “A Monadic Approach to a-solved-problem”.

About this I have an interesting story to tell. Once upon a time, my PhD advisor Amr Sabry tried to reimplement Dan Friedman’s miniKanren (a logic programming language) in Haskell, but he couldn’t figure out how to compose the monads. He asked for help from Oleg Kiselyov, arguably the world’s most knowledgeable person about getting around Haskell’s type system. And if you don’t know, Amr Sabry is probably the world’s most knowledgeable person about purely functional programming languages and side-effects. His paper What is a Purely Functional Language is often referred to as the official definition of “pureness”. After solving the problem with Oleg’s help, they coauthored a Functional Pearl paper. Ironically, Dan Friedman, the original author of that piece of code, didn’t have any such trouble writing it in Scheme in the first place. Certainly there is no reason Amr should be able to figure out how to compose the monads. He and Oleg just wrote the Haskell code for fun, but this story tells me something about monads: they make things unnecessarily complicated.

How did Dan Friedman write the code so easily? He just directly passed the states in-and-out and not using any monads, or you can say that he used monads’ essence without actually using them. Following Dan’s style, I rewrote miniKanren, added constraint logic programming and a highly sophisticated negation operator to it. All this is done within three weeks during my first semester as a PhD student, together with Dan’s B521, Amr’s B522, other course loads and teaching duties. I would certainly be bogged down had I used monads, and I don’t see any point of translating it into a monadic style. It is just so much simpler without monads.

(Correction to some historical facts by request from Prof. Friedman: He’d like to give a lot of the credits of the current miniKanren code’s simplicity to Chung-chieh Shan, who at one moment simplified the code to its current style.)

Equational reasoning can’t save the world

On the safety side, purely functional languages haven’t much advantage either. Some people claim that the value of monads is that they explicitly delimit the side-effects and support equational reasoning, but programs are not always as easy as algebra formulas such as a(b+c)=ab+a*c. If all programs are that easy, we would not need monads at all. Monads don’t really make your program easier to reason about.

Pure functions always return the same results when they are given the same input, but every monadic function has an extra “implicit” argument which is different at every call to the same function, so although it is still true that “pure functions always return the same results when they are given the same input”, the problem is, you never get the same input because of that always-changing extra argument! You don’t know what’s inside that argument. That argument is called the “state”.

There is no way you can statically know the values inside state monads, for the same reason that you don’t know the values inside the heap. This is because the state monads are in essence the same as the heap. The heap maps memory addresses to values, and state monads map variables to values. If you have written static analysis, it will be clear that monadic code is in essence putting parts of a static analysis into the user’s code. In other words, every monadic code is reimplementing part of a static analysis. So monadic code is as hard to analyze as if you use side-effects, only that it takes a lot more work to write. You can write horribly side-effective code with monads which nobody can understand and no static analysis tool can help. There is no such thing monads can make easier which can’t be done by static analysis. Static analysis researchers know this very well.

You can write pure functions in any language

Monads are contagious. Once the code gets into monads, it is not easy to get out. Having to explicitly specify side-effects in the types is similar to having to explicitly declare exceptions in Java. You must either “handle” it, or you must declare that you have passed it on. Why should programmers write them while they can be easily inferred by static analysis? Static analysis use what is essentially monads (or even more advanced techniques), and they take the burden of writing monadic code away from programmers.

Of course overusing side-effects will make programs harder to analyze, but you can reduce side-effects and write pure functions even in an impure language. For example, the following C function is a pure function, satisfying every requirement of the definition of “pureness”.

int f(int x) {
    int y = 0;
    int z = 0;
    y = 2 * x;
    z = y + 1;
    return z / 3;
}

Advanced static analysis tools would have no trouble figuring out things about this kind of code. They would know that this function is pure without you writing any annotations, and they can do a lot more for you than this. So pure functions don’t just belong to purely functional languages. You can write pure functions in any language (including assembly), but the point is, you should be allowed to use side-effects too, especially when they make things easier.

Thinking critically about mathematics as a language

Looking back into history, the dogma from mathematics is the driving force behind purely functional languages. Mathematical functions are simple and beautiful, but unfortunately they work well only when the thing you are trying to model is pure by nature. Purely functional language proponents like using buzzwords like “category theory”, and call those who don’t understand it “uninitiated”. I know a considerable amount of category theory. Even the category theorists themselves call it “abstract nonsense”, because it is to a large extent a grotesque way of saying what other mathematicians already know, in much the same sense that GoF design patterns are a grotesque way of saying what most decent programmers already know. So category theory is the analogous of design patterns in mathematics.

If you read Gottlob Frege’s article Function and conceptyou will be surprised that most mathematicians got functions wrong before his writing, and that was just a little more than a hundred years ago. Mathematics have done lots of things wrong with its language. This has been pointed out a long time ago by Gerald Susman in his Structure and Interpretation of Classical Mechanics and recently in his InfoQ talk. There is a lot of truth in his words. There is no reason programming language designers should blindly follow the ways of mathematics, because it is just another quirky language.

What is functional programming, really?

The above is not to disagree with functional programming in general. On the contrary, functional programming in general is highly valued. I just disagree with the dogma of the “purely functional” ones. Impure functional languages such as Scheme and ML haven’t these problems. They have “benign side-effects”. In fact, in Scheme functions are called “procedures”, not “functions”. This is because its designers know that they are not functions in the mathematical sense, and they intended to make them not necessarily pure. The purely functional language community often try to steal the word “functional programming” from traditional functional languages (Lisp, Scheme, ML), as if only purely functional languages deserve the name. This is not fair and this is harmful. We should be able to use the word “functional programming language” to refer to any language with correct implementation of first-class functions.

Don’t fall in love with your model

Everything starts to do harm when they are pursued to the extreme. Purely functional programming tries to fit the world into its model, but the world works in a completely independent way. It is wrong to think of everything as a nail when you have a hammer. Only by observing the reality can we get out of the religions that are limiting us. Don’t fit the world to your model. Fit your model to the world.

 
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Posted by on November 16, 2013 in functional programming, programming languages

 

Null reference may not be a mistake

null

The null pointer is considered to be a “billion-dollar mistake“. I have been wondering why there is such a notion until I saw the video where Tony Hoare claims it to be his mistake. In fact, he didn’t really say that null pointer should not be used.

From this video, you can see that introducing null reference is not really a mistake. On the contrary, null references are helpful and sometimes indispensable. The mistake is not in the existence of the null pointers, but in how the type system treats them. Unfortunately, most languages (C++, Java, C#, …) don’t treat them correctly.

Every class type A of Java is in fact a union type {A, null}, because you can use null where an A object is expected. {A, null} is almost equivalent to the Maybe type of Haskell, where null corresponds to Nothing of Haskell. So the trouble really is that an annotation like {String, null} should be distinguished from String, so that it will be clear whether null can possibly be its value.

Unfortunately most languages don’t provide a convenient union type that you can put String and null together (Typed Racket is an exception). If Java is to have union types, we can say something like:

{String, null} find1() {
  if (...) {
    return "okay";
  } else {
    return null;
  }
}

This is saying: find1 may return a name which is a String, or it may return nothing. Because of the union type {String, null}, the type system knows that you should check for null when you have called find(), so it will force you to write a null check:

String s = find();  
if (s != null) {
  x = s.length();
}

In comparison, if we define a slightly different function find2, with a different return type:

String find2() {
    ...
    return "okay";
}

From the return type we know that find2 will never return null, so the type checker can let you you use the String without checking:

String s = find();
x = s.length();

 
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Posted by on June 3, 2013 in programming languages, types

 

Back to the future of databases

Why do we need databases? What a stupid question. I already heard some people say. But it is a legitimate question, and here is an answer that not many people know.

First of all, why can’t we just write programs that operate on objects? The answer is, obviously, we don’t have enough memory to hold all the data. But why can’t we just swap out the objects to disk and load them back when needed? The answer is yes we can, but not in Unix, because Unix manages memory as pages, not as objects. There are systems who lived before Unix that manage memory as objects, and perform object-granularity persistence. That is a feature ahead of its time, and is until today far more advanced than the current state-of-the-art. Here are some pictures of such systems:

IBM System/38

system-38

Lisp Machine

lisp-machine

Oberon

Oberon

Those systems don’t really need databases (in its usual sense). Data integration was seamless and transparent to the programmer. You don’t need to know the existence of a “disk”, a “file system”, or a “database”. You can just pretend that you can allocate infinite number of objects and work on them in the most natural way. Unfortunately most of those systems were either terribly expensive or had problems in other aspects of their design. Finally, they seemed to have died out.

Good ideas never die. Nobody uses those systems today, but this is not to say that there is nothing we can learn from their design. On the contrary, some of their ways are far superior than the current state-of-the-art of Unix-based systems. Unix will never reach that level of elegance and power.

But any how, Unix rules the world. We can live with it, but it is just mediocre. Please don’t believe everything that the modern Operating Systems books tell you. Sometimes you have to look further into the past for the future. As Einstein said, “Nothing is more needed to overcome the modernist’s snobbishness.”

Unix used to be free, but you get what you pay for. Although there is a thing called “virtual memory”, your programs can’t just allocate objects and then operate on them without any knowledge about the “file system”. Nothing works out-of-the-box in Unix. In fact it is far from that. Unix and its “philosophy” is a constant source of trouble. It is more like a “non-operating system” than an “operating system”. It leaves too much work for you to do, and leaves more than enough rope to hang yourself.

Unix builds its reputation and authority by blaming the users. If you don’t know how to use me, you are an idiot! This is the same trick that the weavers played on the emperor: If you can’t see the clothes, you are either stupid or incompetent. What a powerful way to cover the ass of any crap!

Unix’s incapability is why people “invented” databases. The combination “Unix + databases” is supposed to be a cheap replacement for those advanced systems where programs don’t need to know the existence of such a second-level data storage layer. But because of some irreparable design issues, Unix still can’t achieve that even with the help of databases. The databases, until today, still relies on Unix’s low-tech mechanisms such as memory mapped files to store data, which causes complications and performance issues.

However, databases were somehow considered a big thing, and people who made it became the richest men in the world. Consequently, you have to take database classes if you want a computer science degree. So here is an ultimate cheat sheet for those who really want to know what a database is. You will not need to sit through a semester’s course if you remember the few things that I put below. Trust me, many students got A+’s because I told them this ;-)

Every “row” in a database “table” is a data structure, much like a “struct” in C, or a “class” in Java. A table is then an array (or list) of such data structures. The “keys” of a database table are in essence “persistent memory addresses”. When serializing an object, we can’t just put the memory address of an object onto disk, because the address may not be the same when the object is reloaded into memory. This is why we need “keys”. In a sense, “keys” are a more general notion than “addresses” — addresses are just keys that are integers.

There is a white lie in the above paragraph – I didn’t mention that there is some redundancy in a database table in comparison to a serialized data structure. Some data is duplicated across multiple rows because a RDBMS table row has fixed width, so it can’t store variable length data such as arrays. What can you do then? By recognizing that the table is the only thing that can “grow” in a relational database, an obvious solution is to turn the array 90 degrees clockwise, and make each element a row in another table! But how do you connect from where the array is originated from? You add the key of the object to each row of this new “array table”. See how the key is duplicated? This is why people “invented” column-based databases (such as Vertica, HBase etc) for “compressing” these keys. But what they achieved was essentially making the tables slightly closer to the format of serialized data structures.

You create the problem, and then you solve it. And you call this two inventions.

Keys are persistent pointers. Whenever you need to dereference a pointer, you do a “join” in the database, so “join” is equivalent to “following pointers”.

A database “schema” is in essence a “structure type”, like the struct definition in C. For example, the schema created by the following SQL statement

CREATE TABLE Students ( sid CHAR(20),
                        name CHAR(20),
                        login CHAR(20),
                        age INTEGER,
                        gpa REAL )

is equivalent to the C struct

struct student {
  char* sid;
  char* name;
  char* login;
  int age;
  double gpa;
}

(Note that I use a SQL declaration here just because I don’t want to draw a picture of the schema. This equivalence of a relational schema with a structure type has nothing to do with SQL.)

That’s almost the whole story. You have addresses, pointers, dereference operation, structure types, arrays/lists of structures, so now you can implement things like linked lists, graphs etc. With them, you can implement some complicated algorithms such as A* search in a database. You just need to take a data structure class, and then translate what you learned there into a database language like SQL.

But SQL is a crappy language. It wasn’t designed for programmers. It was designed for manual input by human operators (usually non-technical people like accountants). You type in a “query”, and the computer prints out a “response”. That is why it is called a “query language”. This language does its job for human operators, but it was then abused beyond its capabilities. It was interfaced with computer programs to write serious programs. I doubt if those people knew what they were doing, but it just happened, like many other silly things. There are just so many things you can’t express in that language. The result is a dumb and fragile system held together by band-aids. You have to be very careful otherwise you lose blood.

If you really want to learn SQL, here is the cheat sheet for it:

The query

SELECT Book.title
 FROM Book
 WHERE price > 100

is equivalent to the Lisp expression

(map (lambda (b) b.title)
     (filter (lambda (p) (> p 100)) Book)

This program is then sent to the “database engine” for execution. That is, we move the program to the data, instead of loading the data to the program. And that’s also the principle behind MapReduce. Have you noticed how easy this can be done with Lisp? You just send the code to the interpreters running on remote machines!

The problem with SQL is that you need yet another layer of language before programs can operate the database. SQL is a weak and quirky language. It is not Turing-complete and at some places it doesn’t even “compose”. You need to combine it with a decent language before you can write serious programs. Your programs send SQL commands to the database to store and load data, just like a human operator would do. This is a very low-tech way of data integration. It is error-prone, inefficient and subject to security risks such as “SQL injection”.

Indeed, there is a “good component” in SQL, because it has some “relational programming” features. However, the other word for “relational programming” is “logic programming”, where languages like Prolog and Datalog excel. They are both more expressive and more elegant than SQL. Considering that Prolog and Datalog appeared much earlier than SQL (1972, 1977 v.s. 1986), I would say that SQL is a step backwards.

Maybe you have seen, for some weird reasons we are still in the Dark Ages of computer programming. We are not supposed to be here since better designed systems already existed. It would be foolish to dismiss them as failures. They are just ahead of their times. By looking to the past, we see a way back to the future.

 
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Posted by on April 5, 2013 in data structures, programming languages

 

On pureness

It is usually a pleasure to use a functional programming language, but it is doubtful whether we should care about the “pureness” of the language. To write programs in a completely pure functional programming language (e.g. Haskell) is much like living in a wired world.

There are no electromagnetic waves nor sound waves in such a world, so you don’t have wifi, cell phones, satellite televisions, radios, etc. You don’t even have light or sound. In other words, everything is blind and deaf.

All information must pass through wires or pipes, connected by switch boxes which we call “monads”. You must carefully route all the wires and pipes and connect them correctly before any information processing device, including your eyes and ears, can properly work.

So I think a language will need parts of it not to be pure, in order to naturally represent the effects such as electromagnetic waves. Normally those effects are called “benign effects“.

 
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Posted by on March 31, 2013 in opinions, philosophy, programming languages, semantics

 

A Concise Solution to the P=NP? Problem

To solve P=NP? is to answer the following question:

Can we solve strictly more problems with a computer that does not exist?

Thus we have proved that this problem is nonsense. QED.

Seriously, this blog took me years to conceive, and a week to write. Please don’t take it lightly. If you need a more “authoritative” proof, please refer to this.

 
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Posted by on March 27, 2013 in algorithms, complexity

 

Undecidability proof of the halting problem using lambda calculus

As a teaching assistant for a graduate level “Theory of Computation” course, I don’t understand why we use Turing machines as a model for all the computability and complexity theorems. It is much easier if we just use arguments on functions in a usual programming language. One good choice of such a language is the lambda calculus.

Basically, a function in lambda calculus is equivalent to a Turing machine. The “halting” of a Turing machine is equivalent to the corresponding lambda calculus term reducing to its “normal form”. From this viewpoint, I came up with the following undecidability proof of the halting problem using the lambda calculus.

Proof. Suppose that we have a function Halting(M,w), a hypothetical solver for the halting problem. Halting takes two arguments, a function M and its input w, and it tells you whether or not M(w) will output True. Note that although M may go into infinite loops, never will our magical solver HaltingHalting always returns True or False within finite amount of time.

Now we show a simple contradiction, which proves that the magical solver Halting cannot really exist. This question is: Does the following expression E returns True or False?

E = Halting(λm.not(Halting(m,m)), λm.not(Halting(m,m)))

It turns out that this question cannot be answered. If E returns True, then we apply the function λm.not(Halting(m,m)) to its argument λm.not(Halting(m,m)), and we get

not(Halting(λm.not(Halting(m,m)), λm.not(Halting(m,m))))

Alas, this is exactly the negation of the original expression E, which means E should be False. This is a contradiction (or call it a “paradox” if you like), which shows that the halting problem solver Halting cannot exist, which means that the halting problem cannot be solved.

QED.

To connect back to usual computing theory terminology (as in Sipser’s classic textbook), the functions Halting and M corresponds to two Turing machines, one of which taking the other as an argument. True corresponds to a Turing machine reaching its accept state, and False corresponds to reaching the reject state.

I’m surprised how much shorter this proof is as compared to [Church 1935, 1936] and [Turing 1936]. Actually what I did in the proof was just making a loop in a circuit. Almost every logical paradox has a loop involved–pretty much the same kind of loop, the Möbius strip. Every logic question expects the answer to be one of two sides–either True or False, but the Möbius strip has only one side!

If you hope to learn more on related stuff, a nice book by Neil Jones shows that you can prove every theorem in theory of computation (including computability and complexity) using a simple programming language. It’s not really necessary to use Turing machines for theory of computation. Turing machines make things awkward and complicated.

Now, a fun exercise question may be, what is the connection between the above expressions E with the Y combinator?

λf.(λx.f(x x)) (λx.f(x x))

 
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Posted by on October 25, 2012 in lambda calculus, programming languages, proofs, theory of computation