Tuesday, August 11, 2015

Classes as computational context

Stateful chaos and ways out

Mutable data structures and imperative programming style can quickly lead to incomprehensible programs and significant slowdown in programmer's productivity. The reason is mutability of the data structures: the cognitive burden of having to remember what and when can be mutated, and what these mutations may affect. This becomes more critical as the complexity of code and data structures grows. Simply speaking, as there are more whats and whens, there are even more of what and when combinations from the phrase above: "remember what and when can be mutated". In the worst case, when any 2 program entities can potentially interact directly with each other, complexity grows exponentially in comparison to the number of entities (such as objects, functions, etc.).

There are at least 2 paths that escape from the chaos of stateful programming: introduce some discipline into mutability or give up the mutability altogether. The first approach is what OOP does, whereas the second one corresponds to the ideas of functional programming. We will concentrate on the OOP way.

OOP: disciplined statefulness

I like to think of the core OOP ideas as of means to restrict the arbitrary mutations. For instance, let's say we're modelling car movement in a game. So we have the Car class with data members (fields) like this:

    speed : float
    gear  : int
    rpm   : float
    acceleration : float (from -1.0 to 1.0)

It is clear that we cannot thoughtlessly assign any value to any of the Car fields, right? First, of course, there are restrictions for each individual field. For instance, speed cannot be 1000.0 if measured in mp/h or km/h, and even more, it may not be negative if cars cannot drive backwards in your game. Similar restrictions apply to gear, rpm and acceleration.

Besides of individual restrictions, certain combinations of fields do not make sense for a single car. A fixed gear value implies that there is some well-defined relationship between rpm and speed, right? In fact, gear acts as a proportionality factor for rpm and speed. For instance, on the 1st gear the RPM of 4000 may correspond to the speed of 15 km/h, whereas the same engine speed at the 2nd gear would yield higher car speed, say 30 km/h. We can go further and assume that gear can be 0 for neutral, in which case any relationship between speed and rpm disappears.

So here is the main point of OOP: encapsulation. In other words, bringing restrictions and discipline into mutation. In our car example, there would exist certain methods, such as shift_gear() or accelerate() that know how to change the car instance's state in a meaningful way. Public car's methods are responsible for maintaining class invariants, such as the mentioned relationship between speed, gear and rpm. No one, except Car's methods, can mutate the car's state by direct assignment.

OOP: burden of maintaining invariants

OOP has escaped the total chaos of mutability, but this has its own price: now we should take care to preserve class invariants. As it was just illustrated with the Car class, all the public methods are required to leave the instance they were called on in a valid state.

Let's assume that speed can vary between 0 and 200, gear is an integer from 0 up to 5, rpm is a float 0 - 6000, acceleration is a float from -1 to 1. Let those sets of values be named, respectively, S1, S2, S3 and S4. So speed is an element of S1, gear - S2, rpm - S3, acceleration - S4.

A car object is essentially a tuple of the four values above. So a car object is an element of the set S1 x S2 x S3 x S4, that is, a Cartesian product of all the sets of the class's fields. But, as we have just concluded, not every combination of S1, S2, S3, S4 makes sense as a car object. So in fact, the set of car objects is a subset of S1 x S2 x S3 x S4.

And this is clearly the programmer's responsibility to ensure that the car instance does not jump out of this set. That may sound easier than it really is. For example, an exception may pop out in the middle of a Car's method where you didn't expect anything to be raised. This exception gets caught and the program runs on, but what about the car instance that was being mutated at the time the exception was raised? Is it still an element of the set of (correct) cars, as we just spoke? Or probably it is in an unusable state?

Because of that, it is better to have a class with few fields and many methods than vice versa. And one should think very well before adding a new field to the class. Specifically, one should ask himself/herself: how to initialize the field? what will be the value of this field at the start of each of the existing class methods? when and how can I mutate this field? how will the new field affect the existing class invariants? how to preserve the invariants now that the new field is there?

Why do people like to write classes?

So taking into consideration all the above complications with OOP and classes, I have been asking myself for quite a long time: why do people tend to create a class when they want to do something? Doesn't the word "do" imply that one needs a function, not a class? Indeed, if you can do something statelessly, you should do so. It should be obvious that the functional (stateless) approach is in most cases preferable over the imperative (stateful) one, on the assumption that the code doesn't get considerably less readable if expressed in the stateless style.

For some time, my answer to this question was that people just don't realize very well the potential complications entailed by OOP, such as those described above. Except for that, there's all this "OOP is an industrial standard" crap that drives people from thinking on their own and making right decisions.

Recently, however, I got an insight into this matter. In simple words, people often use classes because they want a bunch of functions to share some data. So they write a class, shove all the things they want to be generally accessible into self (or this, whatever it is called in your language), and then any method can access and mutate anything on self. Pretty smart, isn't it?

Class as computational context

Consider the following example in Python:

class FancyFormatParser:
    def __init__(self, filename, **options):
        self._filename = filename
        self._options = options.copy()

    def parse(self):
        self._file = open(self._filename)
        records = []
        while True:
            record = self._get_next_record()
            if record:
        return records
    def _get_next_record(self):
        self._header = self._parse_header()
        return FancyRecord(

    def _parse_header(self):
        # ...
        # use self._file, self._options for reading
        # ...

    def _parse_name(self):
        # Make use of self._header, self._file, self._options

    def _parse_prof(self):
        # Make use of self._header, self._file, self._options

    def _parse_age(self):
        # Make use of self._header, self._file, self._options

As you can see, the _file attribute is initialized in parse() and subsequently used in those other methods that need to read file data. Same with _header: it is implied that once the header is read and parsed, we store it in a globally accessible place (self), and then methods like _parse_name() can think of _header as of part of the context they are being invoked in.

Alternative: bunch of functions

The reason for such an approach is quite understandable: if we decide to implement the FancyFormatParser above in (almost) pure functional style, then we need to draw values such as _file stream or _header through arguments of all of the functions that need those values. In other words, we would get something like that:

    def parse(filename, **options):
        file = open(filename)
        records = []
        while True:
            record = get_next_record(file, options)
            if record:
        return records
    def get_next_record(file, options):
        header = parse_header(file, options)
        return FancyRecord(
            name=parse_name(file, header, options),
            profession=parse_prof(file, header, options),
            age=parse_age(file, header, options),

    def parse_header(file, options):
        # ...
        # use file for reading
        # ...

    def parse_name(file, header, options):
        # Make use of header, file

    def parse_prof(file, header, options):
        # Make use of file, header, options

    def parse_age(file, header, options):
        # Make use of file, header, options

Did you notice how the code got slightly more verbose? More explicit formal and factual arguments. Although in this example the difference may not seem really big, but oftentimes there can be quite a number of self attributes that would have to be pulled into the methods' arguments. In this case, when you rewrite your methods to be functions with no self and getting all the needed arguments explicitly, you will discover that some of them accept 5> parameters. Which obviously doesn't feel nice.

Improvement: do everything in __init__, if possible

Let's enhance our FancyFormatParser: do the whole job directly in its __init__ method.

class parse_fancy_format:
    def __init__(self, filename, **options):
        self._filename = filename
        self._options = options.copy()
        self._file = open(self._filename)
        records = []
        while True:
            record = self._get_next_record()
            if record:
        self.result = records

    def _get_next_record(self):
        # ... all the same ...

I like this variant much more than the FancyFormatParser class we had before. Here's why. FancyFormatParser was intended to be used like this:

parser = FancyFormatParser('big-castle.txt', length=2048, ignore=True)
records = parse.parse()

Our new class parse_fancy_format is to be used in this way:

records = parse_fancy_format('big-castle.txt', length=2048, ignore=True).result

Can you feel the difference? With FancyFormatParser the intentions were implicit. One instance should have been created and a single method should have been run on it, just one time to do the job. After that, the whole instance was not meant to be used any longer. But that wasn't immediately apparent by looking in the code.

The parse_fancy_format class is more explicit: all its methods are private, so the only thing you can do from outside is to instantiate it. Whatever needs to be done or computed is carried out directly in __init__, and then result becomes available in the attribute with a convential name, for instance, result.

The class is named as function. This is done on purpose: to emphasize that this class is going to be used almost like a function, for one-time computation. This is in contrast to the typical case when an object is deemed to live for some time and have its state mutated by methods.

However, I should agree that this convention of naming classes like functions and storing results in the object attributes is not a common approach. Moreover, the trick with attributes is quite ugly by itself. Nevertheless, this style is yet better than the initial FancyFormatParser class.

Pros and cons

The main advantage of using classes as context for one-time computations in comparison to the top-level function approach is reducing the number of formal arguments. Functions can easily share data by storing attributes on self -- that is, using self like a context. Many people find it really convenient to put things on self and have them accessible from other parts of code. This reduces the difficulty of clearly thinking out dependencies between pieces of data.

The disadvantage is that it is easy to create a standard OOP mess, when there is plenty of self attributes with implicit class invariants which is easy to break.

As a general conclusion, I think the computational context trick is quite viable and certainly has the right to exist. But one should still keep in mind the dangers of OOP described above. So

  • don't shove too much onto self: if you're using some data only in the scope of a single method, put it in into a local variable, not an additional self attribute;
  • if you can clearly see that certain information will be shared between a small set of methods, make it into a formal parameter, don't put on self. Explicit is better than implicit;
  • if there are some objects that should be accessible almost at any point of the computation, then you should definitely make them into self attributes. For example, this can be a database connection or an output stream object.

Sunday, October 27, 2013

Lisp for C++ programmers

For whom?

One old good friend of mine, whom I respect a lot and who is a very good C++ programmer, recently asked me to give him an example of how it's possible make new language features in Lisp. He's aware of Lisp's ability to invent new syntax, and he's also excited about C++11. So he wonders how is that possible to introduce new syntax into your language all by yourself, without having to wait for the committee to adopt the new feature.

I decided to write this article for C++ programmers, explaining core Lisp ideas. It's a suicide; I'm sure as heck that I'll fail. Great number of excellent publications on Lisp for beginners exist, and still there are people who cannot grasp what's so special about it.

Nevertheless, I decided to try. Yet another article with introduction to Lisp won't harm anybody, nor will it make Lisp even less popular. Let's be honest: nobody reads this blog, anyway. :)

Why Lisp matters?

Lisp matters because that's a language which gives a programmer the possibility to extend its own syntax. That's as if you could invent new keywords in C++, for example, or special syntax for std::map literals:

std::map<std::string, int> m1 = {
    ("one", 1), ("two", 2), ("three", 3)

std::map<std::string, int> m2;
m2["one"] = 1;
m2["two"] = 2;
m2["three"] = 3;

typedef std::map<std::string, int>::value_type vtype;
vtype things[] = [vtype("one", 1),
                  vtype("two",   2),
                  vtype("three", 3)];
std::map<std::string, int> m3(
    things + sizeof(things)/sizeof(things[0]));

All the m1, m2 and m3 are equal. The first example features a new syntax for giving std::map literals; I made it up, it doesn't really exist. Just imagine that we could invent it ourselves.

Why Lisp matters for C++ programmers?

Any sufficiently complicated C or Fortran program contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Common Lisp.
Greenspun's tenth rule
And you're right: we were not out to win over the Lisp programmers; we were after the C++ programmers. We managed to drag a lot of them about halfway to Lisp. Aren't you happy?
Guy Steele (on Java)

Lisp has something that C++ has always wanted to have. Lisp is (to some extent) something that C++ has always striving to become. Lisp contains some forgotten ideas which were popular in early days of computing and went into oblivion as programming became more popular. Lisp will give you some useful insights that you won't find anywhere else.

Is Lisp a silver bullet then?

Certainly not. If it were, no new programming languages would have been appearing after 1962.

I won't go into details about deficiencies of Lisp. That's another problem to be discussed; an extremely painful problem, in fact. Just keep in mind that I'm not claiming C++ is shit and Lisp is a rose.

What are fundamental difficulties with understanding Lisp?

If you're a C++ programmer wanting to understand how a language can be so flexible that it enables to introduce new syntax, there are some fundamental difficulties for you to understand Lisp as an instance of such language. That's because Lisp is not "C++ + the ability to define new syntax". Lisp is much different from C++ in ways that have nothing to do with syntactic extensions. I mean, dynamic typing, functions as first-class values, no OOP in the first place, no templates, etc.

When a C++ programmer starts to delve into some Lisp introduction, he usually advances up to the point where Lisp looks completely alien and impractical, and then he's not able to move any forward. Syntactic extensions, as you guess, lie long after the point where the C++ programmer stops.

So, what makes Lisp look alien and impractical to our C++ programmer?

  1. Dynamic typing. The dilemma of static/dynamic typing is one of those half-philosophy-half-programming questions that are not going to be resolved in favor of either side any time soon.

    I believe that Lisp core ideas are incompatible with the idea of static typechecking, at least with mandatory typechecking. I cannot explain why, without explaining those core ideas themselves. Instead, let's try to look at static type systems in the following light.

    A static type system is something non-primary to programming, something additional, ancillary. Imagine an interpreter for a simple toy language: you give the interpreter a piece of code and it just executes (evaluates) the code. Static typing means that before running or compiling, there must be an additional phase of processing – type checking. That's why static typing is not necessary; there are dynamic languages without it, such as Python or JavaScript. As a downside of it, these languages have to perform type checks at runtime. For example, in Python you just write:

    def process(a, b):
        return a + b + 20
    without anywhere mentioning types of a and b. But when "+" gets executed in the course of your program run, it has to make sure a and b are actually numbers.

    Yeah, I know, you're saying that's bad. Having to check types dynamically over and over again instead of just checking them once is bad. I agree to some extent. But I want you to pick up 1 thing: static typing is not something vital to programming. It's not vital in the business of making computer do what you want. Static types are useful and arguably superior to dynamic types, but they are not necessary. It's an additional feature which is good and fine but not necessary.

  2. Lots Of Idiotic Silly Parentheses.

    Lisp has all the visual appeal of oatmeal with fingernail clippings mixed in.
    Larry Wall

    Which is more readable:

    a[x] += b[x-1] + 3 * b[x+1];


    (aset a x (+ (aref a x)
                 (aref b (- x 1))
                 (* 3 (aref b (+ x 1)))))

    Those parentheses seem to be obfuscating everything. Yes, I agree that Lisp is superficially less readable than most traditional languages. "Superficially" means that Lisp looks worse for uninitiated, unprepared and inexperienced people; once you get some experience with it, you learn to see past paretheses.

    But generally, that's true that Lisp looks ugly, especially Common Lisp. Although there are some nicer dialects, like Scheme or Clojure.

    Why does Lisp look ugly to normal people? Ironically enough, this ugliness is the price we pay for being able to introduce new syntax. Lisp cannot have special syntax as C++ does, because in a language where anyone can create new features and DSLs, no syntax is special. In fact, many people claim that Lisp "has no syntax". This really means that Lisp has uniform syntax: every piece of code is just a list delimited with parentheses.

    To know what the list really is and what it means, one must look at its head element:

    • if the head is the name of a function, the list is just a function call form, and remaining elements are arguments to the function;
    • if the head is the name of a special (core) operator, then this list is a special form with special meaning. There's a fixed number of special operators (26 in Common Lisp, 5 in Scheme, about 27 in Emacs Lisp). Special operators roughly correspond to keywords in C++. They are generally these: assignment, looping constructs (like while/until/for), introduction of local variables, lambda, throw/catch. Note that primitive operators like +, -, / and * are ordinary functions in Lisp and are not special in any way;
    • if the head is the name of a macro, the list is a special syntax construct which is to be translated into a special operator form or a function call form (one of the above 2). How this is done is the point of this article and is described below.

    Now I hope you see at least some justification why Lisp is ugly.

  3. Only lists.

    Some folks after initial acquaintance with Lisp make erroneous conclusion that list is the only composite data structure available in the language. Indeed, Lisp stands for "LISt Processing", so it's all about lists.

    No! Lisp programs manipulate all kinds and diversities of data structures; this depends on concrete Lisp dialect you're using. Common Lisp has C-style structures, vectors and growable vectors, multidimensional arrays, strings, complex numbers and even objects and classes.

    So, why are lists special then?

    Lists are special only because code is represented with lists. That's all about them. You can have lists of numbers, of strings, of anything you want (lists are heterogeneous because of dynamic typing). And a piece of code is also a list! That's why lists are special. Code can be manipulated as data – that's the cornerstone of Lisp, its heart.

    When you regard a list as code, you typically call it "a form". So "form" means "list which is treated as code".

  4. It is not compiled

    Some C++ programmers (I believe not very many of them, by now) can hardly imagine how it's possible not to have a phase of compilation. If you're one of those, I'm trying now to convince you: compilation is not necessary, much in the same way as static typing is not necessary.

    What is compilation? It is translation into low-level code. There are 2 ways to run a program: either run it directly with a special runner, or have it translated into machine-level language and run it directly by the hardware. The first way is interpretation, and the "runner" is conventionally called "an interpreter"; the second way is compilation, and the program which performs translation is compiler.

    The distinction between interpretation and compilation is not strict. Consider byte-codes. Your program can be compiled into byte-code, and the byte-code is interpreted by a special byte-code interpreter. Moreover, there's also JIT which means that compilation can take place on-the-fly and is optional.

    C++ is a performance-oriented language. It is unthinkable how it can be interpreted. Or is it not? Consider debuggers: they allow you to enter arbitrary C++ expressions into the Watches window. Each time the debugger stops, the value of expression is reevaluated and displayed into that window. How does the debugger do it? The debugger interprets the expression. Oh, excuse me: it can actually compile it, and then rerun the code each time it needs to. In this case, debugger is somehow able to compile C++ code on-the-fly, and run it.

    I believe you're a little bit more convinced now that even in C++ compile/interpret distinction is not very firm.

    Compilation is not necessary: it is a preparational step aiming to improve performance of your program by translating it into lower-level language. C++ is special because it targets machine language for performance reasons, so compilation in the case of C++ is necessary. But it's not necessary in the general case.

    Lisp can be both compiled and interpreted (even simultaneously); this depends on the implementation of a concrete dialect. For the purpose of this article, I won't talk about compilation of Lisp code except places where I intend to touch it explicitly. You can assume from now on that Lisp is interpreted, because thinking so is easier to get the idea of how it works. I promise I'll give special attention to compilation later.

Heart of Lisp: code is data

Enough about difficulties with Lisp. Let's get to Lisp itself.

In C++, your code is completely gone once it's compiled. Code is just a piece of text which is consumed by the preprocessor and compiler and is transformed (translated) into some machine-dependent representation and then executed.

In Lisp, code is live. Code is represented with certain data structures that you can manipulate by means of other code. Code is not gone when you compile your program. This opens up the possibility to implement new language features and do metaprogramming. You can write code that writes code, because "writing code" in Lisp is no different than "creating lists", and "running code" is the same as "evaluating lists".

By the way, in Lisp terminology, "evaluating" code means just "running" or "interpreting" code.  Evaluation is orthogonal to the compilation/interpretation dualism.  Evaluation has to do with carrying out computations; the compilation vs. interpretation thing is about how to carry out computations: directly or via preliminary translation.

Lisp is thus self-hosting: your Lisp program can create new Lisp programs or modify itself. Lisp has no compile-time/run-time distinction, and that's what the power of Lisp is all about. Even if a Lisp implementation provides compiler, there's still no compile-time/run-time dualism: you can run arbitrary Lisp code during compilation, and you can call compiler during the run-time of your program. That means you can bake functions out at run-time and compile them (with all optimizations), and then call them.

Evaluation of function call forms

So, now that you're supposed to be intrigued, let's talk about how code is actually represented as data structures, and how to do metaprogramming. Be patient: the trick is extremely simple, but unfortunately it cannot be explained as simply.

We shall begin with the notion of evaluation. As you know, in Lisp code is data, and "to run code" means "to evaluate data". Any kind of datum can be evaluated. But lists, as you guess, are of special interest.

Consider this piece of code:

(+ 10 20)

That's a list consisting of three items. The first one is the symbol "+", the second is number 10, and the third is number 20. (You don't know yet what "symbol" means, I'll get to it later. For now, symbol is a data type by which variables and identifiers are represented in programs.)

Let's enter (+ 10 20) at the REPL (Read-Eval-Print Loop). I'll use Emacs Lisp:

ELISP> (+ 10 20)

We see that (+ 10 20) has evaluated to 30. How was that done? Look at the bulleted list above, where I showed possible kinds of forms. We have a list; its head element – symbol "+" – is the name of a (primitive) function that adds numbers. So this list is a function call form. The other 2 items are arguments: they are passed to the function, which adds them and returns 30. Pretty simple, yes?

ELISP> (+ 3 (* 2 4))

This is also a function call form. But the third item of the list is itself a list (a nested list). This means that it must be evaluated before passing to the "+" function. So, the evaluation is carried out this way:

(+ 3 (* 2 4)) → (+ 3 8) → 11
ELISP> (+ (- 2 3) (* 2 4))

That was also quite intuitive:

(+ (- 2 3) (* 2 4)) → (+ -1 (* 2 4)) → (+ -1 8) → 7
ELISP> (concat "I love " "programming"
                  (concat " despite of " "my" " age"))
"I love programming despite of my age"

(concat "I love " "programming"
         (concat " despite of " "my" " age")) →
(concat "I love " "programming" " despite of my age") →
"I love programming despite of my age"

This is how function call forms are evaluated in Lisp: first the arguments are evaluated, in first-to-last order, then the function call is made. Arguments can be arbitrary expressions.

ELISP> "Luck"

Simple numbers and strings are evaluated to themselves.  In other words, they are self-evaluating.

Data types

A Lisp system operates with objects (not in the C++ sense); any datum is an object. Object have types stuck to them at run time (duck typing). Main object types are these:

  • a number (integer or floating-point, for instance)
  • a string
  • a cons cell (a pair)
  • a symbol

As it was mentioned above, all Lisp dialects allow for much wider range of types. But these 4 are exceptional, because they're indispensable and a key to the idea of Lisp. That's why we focus on these 4.

Numbers and strings are ordinary types, just like numbers and strings in any programming language. Strings are generally mutable in Lisp, as in C++.

A cons cell (or a pair) is just an ordered pair of Lisp objects. First object and second object, which are historically called "CAR" and "CDR". Cells are implemented as a pair of pointers. Very simple: just 2 pointers.

Cons cells are important because that's what lists are made of. In Lisp, lists are singly-linked. A list is just a cons cell whose CAR contains a pointer to arbitrary Lisp object, and whose CDR contains either pointer to the next cons cell or NIL, which is a special thing (symbol) to denote empty lists:

Consider this:

struct cons_t {
 int    car;
 cons_t *cdr;

Lisp cells are somewhat like above cons_t structure. But there's one important difference: this is just a convention that CDR was chosen to store a link. You should always keep in mind that CAR and CDR of a cons cell can contain anything.

Generally speaking, cons cells make arbitrary tree structures:

A symbol is a structure with 4 slots:

  • name
  • value
  • function value
  • property list

Slots can be accessed with certain functions that accept symbol as the sole argument. Name is an immutable slot and always contains a string which is the name of the symbol. All the other slots are mutable.

Symbols are important because they are what identifiers are represented with. When you implement new Lisp syntax, you're generating trees of cons cells which contain symbols, numbers and strings at some definite places.

(If you know some Ruby, then Lisp symbols are exactly the same thing as Ruby symbols.)


When you enter an expression at the REPL, the first thing which is done to it is reading. "Reading" means transforming a piece of text that you typed in into Lisp data.

When you enter a number or a string at the REPL, corresponding Lisp object is created and then evaluated:

  234    reads as  <Lisp number 234>
  "Luck" reads as  <Lisp string Luck>

Reading of cons cells is a little bit more complicated:

(a . b)    reads as:

(a1 a2 a3 a4) reads as:

(a1 a2 a3 . a4) reads as:

That is, lists are read recursively. As soon as an open parenthesis is encountered, the reader makes a recursive call to itself to read the next object, whatever it is. The dot is used to delimit CAR and CDR in a cell.

A symbol is produced when the reader encounters something that doesn't look like a number and doesn't start with parenthesis.

number-of-times reads as <Symbol named "number-of-times">
name          reads as <Symbol named "name">
your-age      reads as <Symbol named "your-age">

Symbols are interned, in the same way as string literals can be interned by some C++ compilers. More exactly: there can be at most 1 symbol with a given name. Let S be a string; if a symbol with the name S does not exist yet, then it will be created by the reader when it tries to read S for the first time. After this moment, whenever the reader reads S again, it will produce the same symbol.

To illustrate the point of symbol interning, let's use the eq function; it tests any 2 Lisp objects for identity (and is typically implemented as just pointer comparison):

ELISP> (eq (read "your-age") (read "your-age"))
(Here, we did actually call the function read explicitly. This is the same function which is called implicitly by the REPL implementation when it reads our input. So there's nothing unusual here.)

You see that reading 2 equal strings produces the same Lisp object. "t" stands for "true", and "nil" is "false": these 2 are special symbols.

Symbols are different from cons cells and strings with respect to reading: when strings and cons cells (lists) are read, fresh objects are produced each time. See this:

ELISP> (eq (read "\"vasya\"" "\"vasya\"")
ELISP> (eq (read "(10 20)") (read "(10 20)"))
ELISP> (eq (read "(10 . 20)") (read "(10 . 20)"))
ELISP> (eq (read "vasya") (read "vasya"))

Symbols in Lisp correspond to identifiers in other languages, but because of Lisp's liberal reader syntax, symbols can contain all characters except for some special ones, like parentheses and quote ('):

ELISP> (read "1+1")
ELISP> (read "number->string")
ELISP> (read "class%")

Evaluation of symbols

Earlier I said that any Lisp datum can be evaluated. You've learned that strings and numbers are self-evaluating. Symbols are different: they evaluate to their value slot. That is, when Lisp evaluates a symbol, the result is whatever is stored in its value slot. For example:

ELISP> your-age
*** Eval error *** Symbol's value as variable is void: your-age

ELISP> (set 'your-age 12)
ELISP> your-age

ELISP> (set 'your-age '(10 20 30))
(10 20 30)
ELISP> your-age
(10 20 30)

The symbol "your-age" had an unbound value slot initially, that's why we got the error. Unbound symbols cause an error to be signaled when they're evaluated. Then we put the number 12 into the symbol's value slot, and evaluated the symbol. The function set accepts 2 arguments: a symbol and any other Lisp object. It stores the object into the symbol's value slot. You'll soon see better ways to give values to symbols.

Evaluation of quote

If you've been attentive enough all that long, you should remember that we've considered evaluation of function call forms, and there are 2 other kinds of forms that we haven't touched yet: special forms and macro forms.

Special forms differ among Lisp dialects. The most important special operator, which is present in all of them, is quote:

ELISP> (quote 20)
ELISP> (quote (i still dont get lisp))
(i still dont get lisp)

ELISP> (quote (20 + 30))
(20 + 30)

ELISP> (quote (+ 30 20 (- 10)))
(+ 30 20 (- 10))

So what is quote doing? Nothing! It's there to prevent evaluation. The syntax of quote is like this:

(quote SUBFORM)

When such a form is evaluated, the result is SUBFORM, without evaluation. Compare these:

ELISP> (quote (+ 20 30))
(+ 20 30)

ELISP> (+ 20 30)

ELISP> (quote (+ 1 2 3))
(+ 1 2 3)

ELISP> (+ 1 2 3)

ELISP> (quote your-age)

ELISP> your-age
(10 20 30)

So quote acts in a pretty straightforward way: it just returns the second element of the list, whatever an object it is. Consequently, for self-evaluating objects quote is not necessary:

ELISP> (quote 20)
ELISP> "love"
ELISP> (quote "love")

Do you see how quote is different from an ordinary function call form? Evaluation semantics is different: for a function call form, first all the arguments are evaluated in order and then the function is called, wherever in the case of a special form, not all arguments are necessarily evaluated. Moreover, the arguments of a special form are typically given certain meaning and are sometimes required to be lists of certain shape. That's what's called syntax in Lisp parlance.

Remember our previous example with reading symbols and comparing their identity?

ELISP> (eq (read "love") (read "love"))
ELISP> (eq (quote love) (quote love))
ELISP> (quote love)
ELISP> love
*** Eval error *** Symbol's value as variable is void: love

When a variable (== a symbol) goes by itself, you get its value; when it is quoted, you get the variable itself. Kind of meta-something, isn't it? It really is. Keep reading.

quote is used quite often in Lisp programming, that's why there's special reader syntax for it: a single quote ('):

ELISP> (eq 'love (quote love))
ELISP> (quote (quote (1 2 3)))
'(1 2 3)
ELISP> (first '(1 2 3))
ELISP> (first ''(1 2 3))

'OBJECT is just an abbreviation for (quote OBJECT). first is a function that returns the first element of a list.

let, let*, progn, if and cond

Let's learn syntax and semantics of some other special operators.

let and let* are like this:

(let (BINDING ...) FORM-1 FORM-2 ... FORM-N)

where each BINDING is a 2-element list (VAR VAL). Each VAR must be a symbol. let is evaluated like this: first all VALs are evaluated in order, then all VARs get bound to their respective VALs (via storing VALs in VARs' value slots), then all FORM-i are evaluated in order. Values of all FORMs except FORM-N are discarded, and the value of FORM-N is returned as the value of the whole let form. After FORM-N is evaluated, all the symbols VAR-n are restored to the values which they had before evaluating let.

let* is like let, but bindings are established sequentially: first VAL-1 is evaluated and stored into VAR-1, then VAL-2 is evaluated and stored in VAR-2, and so on.

(progn FORM-1 .. FORM-n) == (let () FORM-1 ... FORM-n)

progn is Lisp's analog for block statement in C-like languages (curly braces). (progn) is evaluated to nil.

Now branching constructs.

(if TEST THEN ELSE-1 .. ELSE-n).

TEST form is evaluated: if it is nil, then (progn ELSE-1 ... ELSE-n) is evaluated; if not nil, THEN is evaluated. So, for the purpose of testing, all Lisp objects except nil are considered true.

(cond CLAUSE ...)

cond is like a chain of nested ifs. First, TEST of the first clause is evaluated. If it produces true (non-nil object), then all FORM-1 ... FORM-n are evaluated as in progn. In case when TEST is the sole element of its clause (so the clause is 1-element list), then the value of TEST itself is returned. If TEST evaluates to nil, then the next clause is considered, and so on. If no clause succeeds, the cond's value is nil.

lambda and symbols as functions

lambda is not a special operator, it is anonymous function. More precisely, lambda is just an ordinary list which starts with the lambda symbol:

(lambda PARAM-LIST FORM-1 .. FORM-N)

Lists which start with the lambda symbol can be called as functions. When a lambda function is called, all the parameter symbols are bound to respective factual arguments, and FORMs are evaluated as in progn. Then parameters are restored to their previous values.

It is important to understand that lambdas cannot be evaluated (in classical Lisp that I'm talking about in this article). They can appear as head (first) elements of function call forms, just like symbols that designate functions:

ELISP> ((lambda (x) (+ x 10))

We have already seen symbols used as function names in function call forms. This works because symbols can be treated as functions by referring to their function value slot. So, whenever a symbol appears as the head of a function call form, the Lisp system takes its function value slot and uses it as a function (i.e., calls it with the specified arguments).

In other words, symbols are not first-class functions, they're only names of functions. First-class functions are lambdas and primitives. Primitives (subroutines) are present in every Lisp implementation and are typically written in C. Core functions like cons, car, cdr, +, *, eq are typically primitives.

We can examine the function value of a symbol (i.e., contents of its function value slot) via the function symbol-function:

ELISP> (symbol-function '+)
#<subr +>
ELISP> (symbol-function 'eq)
#<subr eq>

Here, #<subr ...> designates subroutine. Subroutines are separate type of Lisp objects, one of those which don't matter for our discussion (because they are implementation-specific).

lambda parameter list

Lambdas accept parameters of the following shape:

(m-1 m-2 .. m-n [&optional opt-1 .. opt-m] [&rest rest])

Details differ among Lisp dialects. In Emacs Lisp, which I'm focusing on, things work like this:

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
        10 20)
(10 20 nil nil nil)

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
        10 20 30)
(10 20 30 nil nil)

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
        10 20 30 40)
(10 20 30 40 nil)

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
        10 20 30 40 50)
(10 20 30 40 (50))

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
        10 20 30 40 50 60 70 80 90)
(10 20 30 40 (50 60 70 80 90))

ELISP> ((lambda (m1 m2 &optional opt1 opt2 &rest rest)
          (list m1 m2 opt1 opt2 rest))
*** Eval error *** Wrong number of arguments: (lambda (m1 m2 &optional
opt1 opt2 &rest rest) (list m1 m2 opt1 opt2 rest)), 1

I hope you get the idea: there are mandatory and optional parameters, and also a special &rest-argument, which is assumed to be the tail of the list which remains after all mandatory and optional arguments have been consumed by their respective formal parameters.

Lisp is Lisp-2

This kind of Lisp is sometimes called Lisp-2, because there are 2 namespaces: for values and for functions, which means that any symbol can be simultaneously a function name and have a value which has nothing to do with its use as a function:

ELISP> (let ((+ 10)
             (- 20))
         (+ + -))

As you know, a symbol which is at the head of a form, is taken its function value, whereas if a symbol appears at any other place, it is evaluated by taking its usual value (the value slot). In the example above, when (+ + -) is evaluated, the first + acts as a usual summation operator, but the other 2 symbols – + and - – are regarded as values. Those values are 10 and 20.

By now, we've seen only how it is possible to call functions which are situated at the head position of a form; the function itself could be either a symbol or a lambda. But what if we want to call a function as a value? For example, we want to make a function which applies some other function to the first two elements of a list:

ELISP> (defun app (f list)
         (funcall f (first list) (second list)))
ELISP> (app '+ '(10 20 30 40))
ELISP> (app '+ '(10 20 30 . 40))

funcall is a special function which calls its first argument (which must be a function) giving it all the other arguments. Being an ordinary function, funcall receives its first argument evaluated. In such a way we can use values as functions.

In the example above, (funcall f (first list) (second list)) is not the same as (f (first list) (second list)): in the first case, we evaluate symbol f in the normal way (by taking its value slot), and then call whatever we got as a function. In the second case, we call the function designated by the symbol f, and this has nothing to do with the argument f that we received.

Manipulation with lists

If you're not asleep and still alive, I've got a good news for you: we have almost come to the point where you're supposed to see how to implement new language features.

But implementing new language features is done via manipulations with lists, so we must first learn some functions that manipulate lists.

Three basic functions to work with lists are cons, car and cdr.

  • cons makes a new cons cell whose CAR and CDR parts refer to the first and second arguments, respectively:
    ELISP> (cons 10 20)
    (10 . 20)
    ELISP> (cons 30 nil)
    ELISP> (cons 30 '())
    ELISP> (cons 'a 'b)
    (a . b)
  • car and cdr return CAR and CDR parts of a cons cell:
    ELISP> (car '(10 . 20))
    ELISP> (cdr '(a . b))

There are also a plenty of other functions. Here are some:

  • list returns a list of its arguments:
    ELISP> (list 10 20 30)
    (10 20 30)
    ELISP> (list)
  • append concatenates all the lists given to it, and returns a single great list:
    ELISP> (append '(10 20) '() '(30 40))
    (10 20 30 40)
    ELISP> (append '() '() '(30 40))
    (30 40)
    ELISP> (append '(10 20) '(a) '())
    (10 20 a)

Evaluation of macro forms

Finally we got to macros. A macro form is a form (a list) whose CAR is a symbol designating a macro. We don't know yet what macros are, so let's talk a little bit about them.

A macro is not a first-class object in Lisp, which is surprising enough. A macro is a syntactic transformer which is created like this:

(defmacro NAME PARAM-LIST FORM-1 .. FORM-n)

Technically speaking, after evaluation of defmacro, NAME's function value slot is assigned a cons cell (MACRO . transformer) – that is, a cons cell whose CAR is the symbol macro (literally), and CDR is a function which is actual syntactic transformer.

When (NAME arg-1 .. arg-n) is evaluated, the Lisp system sees that NAME's function slot contains this kind of cons cell, and knows that NAME is really a macro name, so the whole form is a macro form. What happens now is this:

  • arg-1, .., arg-n are passed unevaluated to the macro transformer
  • whatever the macro transformer returns is assumed to be the new form to be evaluated (including a new macro form, of this macro or another, which is to undergo the same process recursively until something other than a macro form is returned).

So macros are different from functions in 2 crucial ways:

  • they receive their arguments unevaluated. This means that what they get as arguments are actual pieces of code rather than whatever this code has been evaluated to
  • they return not a final value but a piece of code which is to be evaluated in place of the original macro form.

Examples of macros

Let's see some (very simple) examples of macros:

ELISP> (let ((a 10))
         (when (> 12 10)
           (set 'a (* a 10))

When is like this: (when TEST a-1 .. a-n). If TEST passes, all a-1, ... a-n are evaluated as in progn. If TEST is nil, then the whole when form returns nil.

When's counterpart is unless, which works the other way around with respect to TEST:

ELISP> (let ((a 10))
         (unless (> 12 10)
           (set 'a (* a 10))
ELISP> (let ((a 10))
         (unless (< 12 10)
           (set 'a (* a 10))

So, how would you implement when and unless? That's simple:

(defmacro when (test &rest forms)
  (list 'if test (cons 'progn forms)))

(defmacro unless (test &rest forms)
  (cons 'if (cons test (cons 'nil forms))))

See what when and unless are doing? They're making lists out of cons cells. Lists of certain structure. We can see what when and unless are expanded to:

ELISP> (macroexpand-1
         '(unless (< 12 10)
            (set 'a (* a 10))
(if (< 12 10)
  (set 'a (* a 10))

ELISP> (macroexpand-1
         '(when (< 12 10)
            (set 'a (* a 10))
(if (< 12 10)
      (set 'a (* a 10))

In this case, they got expanded into an if special form. So when and unless are expressed in terms of if.

More advanced macro: stopwatch

Stopwatch is a special syntax for measuring how long a piece of code takes to execute:

 ... SOME CODE ...
 ... AND CODE ...
 ... AND MORE CODE ...)

This returns how much time was spent executing this piece of code (which is evaluated like progn):

ELISP> (stopwatch (list 1 2 3))

Stopwatch is implemented this way:

(defmacro stopwatch (&rest forms)
  `(let* ((start (float-time)))
     (progn . ,forms)
     (- (float-time) start)))

You see some new reader syntax here: it's called quasi-quoting. Instead of a usual single quote, there's a backquote which is placed in front of a list structure. It functions in exactly the same way as a single quote does, but additionally it's possible to mark some parts of code (at arbitrary depth in the tree) to be evaluated. This is done with comma and is called unquoting:

ELISP> `(1 2 3 4)
(1 2 3 4)

ELISP> `(1 2 (+ 3 4) 5)
(1 2 (+ 3 4) 5)

ELISP> `(1 2 ,(+ 3 4) 5)
(1 2 7 5)

ELISP> `(1 2 (+ ,(* 3 3) 4) 5)
(1 2 (+ 9 4) 5)

More exactly, a "`" (backquote) quotes a form, except for nested subforms marked with "," (comma) which are evaluated.

The reader transforms backquote into some system-defined macro, and this macro, when expanded, analyzes the cons tree looking for nested commas. According to where commas are placed, the code is transformed to use some well-defined functions on lists, like append, list and cons above, and of course ordinary quoting (with single quotes). The resulting code, when evaluated, produces the specified list structure; forms marked with commas are evaluated:

ELISP> (macroexpand-all '(defmacro stopwatch (&rest forms)
         `(let* ((start (float-time)))
            (progn . ,forms)
            (- (float-time) start))))
(defmacro stopwatch (&rest forms)
  (cons 'let*
       (cons 'progn forms)

macroexpand-all is a function that expands all the macros in a cons tree (working recursively to the full depth of it).

In this example, forms was unquoted and that's why you see forms being evaluated above. All the other parts of the tree are quoted with usual quotes.

In other words, backquote and unquote are Lisp's template system.

Unfortunately, I cannot give more examples of what can be done with Lisp macros, because this article got very large and there are lots of much better sources where you can get this information. The list of recommended reading is at the bottom of the article.

As a summary, I'm going to say that implementing new syntax in classical Lisp is not very easy. It's all about manipulating cons cells, and much of this work is done via quasiquoting which we have just used. There is some (great!) further work in this direction, such as Scheme programming language, which is arguably a next-generation Lisp. But for the purpose of this article, you can consider yourself enlightened if you understood how this is at all possible to write code that writes code.

Lisp is not ultimately unique in its class. Things that are naturally connected with Lisp include:

  • XSLT which is XML which processes other XML
  • JavaScript Function constructor, which accepts function body as a string and compiles it into a Function object
  • any scripting language supporting eval
  • the Tcl programming language.

Macros and compilation

Macros have special feature that has to do with compilation: when Lisp code is compiled, macros are expanded (as if with macroexpand-all). I mean, they're expanded at compile time. And you know that macroexpansion is operation that can run arbitrary Lisp code for the sake of producing expansion. So macroexpanders are pieces of code which run during compile time.

As I promised, a couple of words about Lisp compilation. Lisp can be compiled, and Common Lisp, Scheme, Clojure and all the other mature Lisps actually are. Common Lisp even allows optional type declarations which are used by the compiler to produce more effecient code. I believe JIT compilation is a very important technique for improving performance of any dynamic language, and this technique has not yet been explored sufficiently well. JavaScript seems to be the first dynamic language which was considerably sped up by employing clever JIT compiler optimizations.

Modern Lisps

What was described in this article is a kind of classical Lisp of 1962. I used Emacs in examples, but I didn't use any Emacs-specific features. This flavor of Lisp is primitive and lame, the barebone Lisp. For example, there are no native support for closures in such a language. Closures and lexical scoping first appeared in Scheme among Lisp dialects.

Since 1962, the whole family of different Lisps have been created. They all share the same trait: representing code as data and ability to manipulate this data. But there are very many points in which they differ. That's because the word Lisp doesn't mean something fixed, rigidly defined. The word really stands for a single idea, and there exist many ideas other than this which can be implemented in a single language. Many of those are mutually exclusive, like dynamic vs lexical scoping, and there are Lisp dialects based upon dynamic scoping and lexical scoping.


As I mentioned earlier, I don't expect this article to convince more than probably 2% of C++ programmers who are going to read it. That's not because C++ programmers are stupid, certainly. Rather because it is hard to explain things that people are unlikely to have come across anywhere else before.

Thanks for reading.


Thursday, July 25, 2013

Customizing the mode line: relative path

Some time ago I thought that it might be useful if the mode line of
buffers showed not only the buffer name (which is just the file name
most of the time), but also a piece of information about location of
the file.  For example, relative path with respect to some fixed
ancestor directory.

I found this useful when working on my first Ruby gem (an exercise).
I often had to type M-x pwd to see what file I'm editing.


If you're a curious reader who wants to have exhausting information
right now, I send you here. This is GNU info documentation on the
mode line format which Emacs uses to display the mode line (the mode
line is the bottom bar that you see in each buffer).  Certainly, you can
read everything from inside Emacs, with info reader.

So, most buffers use the same mode-line-format, which has complex
structure and allows for deep customization.  Ultimately, it is possible
to assign to mode-line-format anything you want (any valid format).
In this case, you would replace all the functionality which is made
available by the standard format with your one.

We won't go this way, as there are some better alternatives.  Let's look
at the value of this variable:

The thing that we need is the (buffer-local) variable
mode-line-buffer-identification.  By default, it is equal to (#("%12b"
...)), where by "..." I mean some string properties.  The string
literal "%12b" means "buffer name padded with spaces to 12
characters".  The text properties make it possible to switch among
buffers with the mouse and view context help when the mouse is over
buffer name:

So, what we're going to do is to leave the text properties with no
change.  The string itself should be changed to what we need.  Here's
an example of a function which does the trick:

(add-hook 'find-file-hook 'eld-adjust-mode-line-to-show-relative-paths t nil)

(defun eld-adjust-mode-line-to-show-relative-paths ()
  (assert (singletonp mode-line-buffer-identification))
  (let ((rel-name (file-relative-name buffer-file-name
    (unless (string-prefix-p ".." rel-name)
      (setq mode-line-buffer-identification
              (apply #'propertize
                     (text-properties-at 0 (car mode-line-buffer-identification))))))))

"/path/to/base/directory" is hard-coded, which is okay for the first
version.  The logic, as you see, is very simple: 1) compute relative path
to the base directory (it can be anything), 2) if it does not start
with "..", then we're inside that directory's subtree and should
change mode-line-buffer-identification.  Text propeties are copied into
the new string. (We exploit the fact that they are the same for the whole
string, that's why it's enough to take propeties of the 0th character only).
Otherwise, do nothing.

Our function gets added to the find-file-hook in order to operate when a
new file is opened.


Of course, much better solution would be to maintain, say, a list of
directories which are considered to be "base".  Then, in
eld-adjust-mode-line-to-show-relative-paths, we will be checking the
buffer-file-name against each of the directories and will be looking
for the closest one that contains the current file.

Sunday, April 28, 2013

GoF Design patterns and JavaScript: The Builder pattern

[Edit: as some people pointed out, this article got overly big, and I decided
to cut it.  Pieces of text that were thrown away were mostly my contemplation
on how Java and C++ are bad and JS is good, so there's really nothing you
miss since the previous version.]

Stone Idols

I detest to hear people talk about design patterns as an opposite
to.., you know, "ordinary programming".  What a nonsense, god damn it!
You can either make software "in a usual way" or use patterns, and the
second way is widely considered to be much more respectable.

Of course, none of decent programmers make this ridiculous artificial
difference between usual and non-usual programming.  Most realize that
there can be tools and abstractions of differing power, but this
increase in complexity and power is quite gradual, like any other
phenomenon in the nature.

The reason why some people imagine design patterns as being something
special is that design patterns look smart.  They look complex enough
for quite a great fraction of programmers not to be able to easily
comprehend them.  That's why some folks tend to worship them.  Maybe
somewhat like ancient heathens worshiped natural forces they didn't
understand well enough to be able to explain rationally.

And the reason why design patterns look smart is that they push crappy
languages like C++ or Java to their limits.  I mean, the old good Gang
of Four book presents abstractions that are nearly as high-level,
cute, powerful, convenient, etc. as C++ (which was the main language
for the patterns to be implemented, at the time of writing) is
ultimately capable of.

So the patterns are great so much as one is approaching the boundary
of a relatively limited primitive world he or she lives in.  That's
exactly my point.

What JavaScript has instead of patterns?

Well, the real misunderstanding and confusion arise when people with
this kind of pattern-oriented statically-typed thinking find
themselves entangled into JavaScript.  It turns out that "normal"
object-orientation is not supported in JS, neither is static safe
typing; there's no such a thing as "interface", and any function can
be used as a class, which sounds crazy (probably it really is).

The endless stream of complains about JavaScript.

This is not to deny that the language really has some design problems.
In fact, you can find a lot of criticism on the web.  Most of it is
true, I think.  But what I really want to say is that JS doesn't need
all those Java-like things (mentioned above) to get the job done.  JS
presupposes dynamically-typed and function-oriented thinking.  Once a
programmer understands the language, he begins to like it and becomes
more productive.

Now get down to business.  I want to implement classical design
patterns in JS.  More exactly, I wanna show how it is possible to
implement equivalent functionality in JS.  That's what this post is

You will see shortly that, putting details back, JavaScript has
essentially one major paradigm that's powerful enough to substitute
for all the design patterns.  That paradigm is called Higher-Order
Functions.  A related feature which is extremely important is Lexical
Scope.  Besides that, JavaScript is dynamically-typed which gives
great flexibility and saves a programmer a lot of unnecessary
troubles.  The drawback is arguably lesser safety and worse
performance; both are not critical, as practice shows.


"Builder" is an interesting pattern.  Assume that we know a
construction protocol for a thing and we'd like to abstract off actual
representation of the thing.  That's basically the whole sense of the

In "Design Patterns" book by Gamma et al., they suggest the following

The classical book says:

"Use the Builder pattern when:

    * the algorithm for creating a complex object should be
independent of the parts that make up the object and how they're

    * the construction process must allow different representations
for the object that's constructed."

At Wikipedia, there's an example with pizzas.  Honestly, the example
is so much distant from real-life programming experience that I do not
even want to touch it any more.  Let's deal with something real.

Suppose we want to present some graph structure, such as a map showing
interconnected cities.  The cities correspond to vertices and roads
(highways) between them are edges, as usually.  In the context of
JavaScript, we may want to show this thing by means of SVG or HTML 5
Canvas graphics, or even in raw HTML 4 where cities are represented
with <div>s with rounded corners -- this doesn't really matter.

That seems reasonable to employ the builder pattern here; interface
would be like this:

var mbuilder = new MapBuilder();
mbuilder.add('New York', 'Boston', 305.83);
mbuilder.add('Boston', 'San Francisco', 4336.82);
var map = mbuilder.get();
use(map.dist('New York', 'Boston'));

In this way, we only specify cities (identified by string names) and
distances; we abstract away how the graph is stored in memory.

Builder: implementation number 1

For example, one possible data structure that could have been used
here is just a single great object which is used like this:

var distance = map['Boston']['San Francisco'];

In this case, mbuilder.add() implementation is quite simple:

function add(city1, city2, distance)
   map[city1][city2] = distance;
   map[city2][city1] = distance;

And the whole implementation would be something like the following:

function MapBuilder1()
   var map = {};

   this.add = function (city1, city2, distance) {
                map[city1][city2] = distance;
                map[city2][city1] = distance;

   this.get = function () {
                 return {
                    dist: function (city1, city2) {
                             return map[city1][city2];

Builder: implementation number 2

But you can easily think about some more elaborate needs and more
complex data structures.  Say, there's a necessity to get an array of
all cities at any given point of time during construction, and after
construction is complete.  Some external (library) code may require
it.  Thus, the above implementation is not good, because it has to
create and return a new array of cities every time it is called.
That's O(n).

We should separately store an array of cities mentioned so far.  The
new implementation looks like this:

function MapBuilder2()
   var map = {};
   var cities = [];

   function ensureCityPresent(city)
      var tem = cities.indexOf(city);
      if (tem === -1) {

   this.add = function (city1, city2, distance) {

      map[city1][city2] = distance;
      map[city2][city1] = distance;

   this.get = function () {
      return {
         dist: function (city1, city2) {
            return map[city1][city2];

         cities: function () {
            return cities;

   this.cities = function () {
      return cities;

Builder: implementation number 3

Probably someone would need to represent cities as separate objects.
For instance, the interface may be this:

var ny = map.city('New York');
assert(ny.name() === 'New York');
assert(ny.dist('Boston') === 305.83);
var cities = ny.connectedCities();
assert(cities[0] === 'Boston');
assert(cities[1] === 'San Francisco');
assert(ny.numCities() === 2);

So here's still more complicated implementation:

function MapBuilder3()
   var cities = [];

   // Implementation of the City "class".
   function City(name)
      this.map = {};
      this.name = name;

   // These are methods that get attached to every city through the
   // prototype.  Cities are retrieved from the map this builder
   // produces.
   City.prototype.name = function () {
      return this.name;

   City.prototype.dist = function (cname) {
      return this.map[cname];

   City.prototype.numCities = function () {
      var count = 0;
      for (var key in this.map) {

      return count;

   City.prototype.connectedCities = function () {
      var res = [];
      for (var i = 0; i < cities.length; i++) {
         if (cities[i].name in this.map) {

      return res;

   function findCityByName(city)
      var i = 0;

      for (; i < cities.length; i++) {
         if (cities[i].name === city) {
            return cities[i];
      return null;

   function ensureCityPresent(city)
      var tem = findCityByName(city);
      if (tem) {
         return tem;
      tem = new City(city);
      return tem;

   // Implementation of a map's methods.
   this.add = function (city1, city2, distance) {
      var cityObj1 = ensureCityPresent(city1);
      var cityObj2 = ensureCityPresent(city2);

      cityObj1.map[city2] = distance;
      cityObj2.map[city1] = distance;

   this.get = function () {
      // Return the final map now.
      return {
         cities: function () {
            return cities;

         city: function (name) {
            return findCityByName(name);

   this.cities = function () {
      return cities;

Comments on the implementations

You can see that all the above code snippets are based on some core
abstractions.  More precisely, they're based on composable data
structures (which are objects and arrays, in JS) and higher-order
functions that capture their environment at the moment of creation
("closures" is what they are called).

Look at MapBuilder1 again.  You can see that the function add captures
the variable map.  So the value that map had when MapBuilder1()
returned doesn't cease to exist.  It is captured by the function which
is stored in add property, and thus won't be garbage-collected for
at least as long as this function itself is not garbage-collected.

In MapBuilder3, look at the City function.  It is used as class, via new
operator.  City is nested with respect to MapBuilder3, which means tha
each invocation of MapBuilder3 produces a new class.  Think how
awesome is that: we create distinct types at runtime!  We're able to do pretty
much everything at runtime, on the fly, and use all the tools and
abstractions we have, and combine them in any fashion.  Okay, back to
MapBuilder3: it returns a map with 3 methods: add, get and cities.
Add and cities are supposed to be used when building is not yet
finished, and get is supposed to be called once the building process
is done.  So get returns a map which is able to return cities with its
city() method.  Consider this:

var b1 = MapBuilder3();
// ...use b1 ...
var m1 = b1.get();

var b2 = MapBuilder3();
// ...use b2 ...
var m2 = b2.get();

Now, m1.city('New York') is not even of the same type as m2.city('New
York'); those kinds of cities are considered distinct as they're
produced by different builders.  This calls for better locality and