2010-05-20

List Comprehensions

A list comprehension is a compact syntactic form for a list (or array) that is built from applying an operation to certain elements of an existing list (or array). For example:

[7*x-3 | x in 1..n | x mod 3 == 1] 

means the list of all values made by computing 7 * x - 3, for each x in 1 through n where x mod 3 is 1. If n is 10, for example, the generated list is [4, 25, 46, 67]. The three parts of the comprehension are called the output (expression), the input (range) and the filter (predicate).

Common uses of comprehensions

[7*x-3 | x in 1..n | x mod 3 == 1]  // operate on (map) and filter a range 
[7*x-3 | x in a | x mod 3 == 1]     // map and filter an existing list
[7*x-3 | x in 1..n | true]          // no filtering, just map
[x | x in 1..100 | isPrime(x) ]     // just a filter, no map

Sketches

{7*x-3 | x in 1..n | x mod 3 == 1}
[7*x-3 for x in a where x mod 3 == 1]
[7*x-3 for x in a if x mod 3 == 1]              // Python
[7*x-3 for each (i in a) if (x % 3 == 1)]       // JavaScript 1.7 (uncommon)
for (i <- (1 to 10) if x % 3 == 1) yield 7*x-3  // Scala
[7*x-3, x in 1..n, x mod 3 == 1]
{7*x-3 : x ∈ 1..n ∧ x mod 3 == 1}               // Plain old Math!!
[7*x-3 : x ∈ 1..n, x mod 3 == 1]
[7*_-3 | a | _ mod 3 == 1]                      // implicit variable

Complex input sets

How do we handle the idea of two range variables for the input set? We can write two range expressions or range over a set of tuples:

[2*x+y | x in 1..n, y in 'a'..'z' | x mod 3 == 1 and isVowel(y)]
[(x, y*y) | (x, y) ∈ a × (1..10) | x < y]
[x + y for x in a for y in b]                   // Python

Life without comprehensions

If you don't have comprehensions, or a compact, symbolic list append operator, you end up writing this:
List<Integer> a = new List<Integer>();
for (int x = 1; x <= n; x++) {
    if (x % 3 == 1) {
        a.append(7 * x - 3);
    }
} 
Many programmers like that kind of coding. More verbose, but everyone can understand it.
In languages that treat for and if as suffixes to simple statements (like Perl and Ruby), we get compact forms that can be nearly as terse as comprehensions:
a = [];
for x in 1..n
  a << 7 * x - 3 if x mod 3 == 1
end
a = [];
a << 7 * x - 3 if x mod 3 == 1 for x in 1..n
a = [];
a << 7 * x - 3 for x in 1..n where x mod 3 == 1

And, of course, there are map and filter (or select as it is called in Ruby)...

(1..n).filter(x -> x mod 3 == 1).map(x -> 7 * x - 3)
(1..10).select{|x| x % 3 == 1}.map{|x| 7 * x - 3}         // Ruby
(1 to n) filter { _%3==1 } map { 7*_-3 }                  // Scala
map((x -> 7 * x - 3), filter((x -> x mod 3 == 1), (1..n)))

Try the previous examples with your favorite form of lambda expression.

Here's an interesting variation, in Ruby that uses map but not select. Instead we add a if clause to the map, which generates extra nils, which we squeeze out with compact. Not pretty, but it gets that nice little "if" in there. Fun.

(1..n).map{|x| 7 * x - 3 if x % 3 == 0}.compact

Information Hiding

Information hiding occurs when a language allows some program entities to be invisible to parts of a program. When applied to data within an object or module, we usually use the more specific term encapsulation. Information hiding is a good thing since it can make it harder to write certain types of mailicious code, and make it harder to accidentally ruin parts of a system you didn't mean to touch.

Here are some different language forms for information hiding.

Explicit information hiding

A direct approach is to use a modifier — a keyword or symbol that defines an access level for an entity. Here are various possible forms:

private var x;
protected double x;
private protected var x;
package protected boolean x;
package local var x;
public array of int x;
x: public string;
-int x;
+int x;
-(int) x;
+(int) x;

These modifiers can be used to hide a class within a package, a member within a class, or just about anything within a module. Visibility of fields for example, can be restricted to

  • The object in which it appears
  • All objects of the same class in which it appears
  • The package in which it appears
  • Its class and all its class's subclasses
  • Its class and subclasses and the same package

...and it can have no restrictions at all (this generally uses the modifier public).

For languages that favor symbols over words, you could use something like

  • - for most-restricted (private)
  • # for semi-restricted or (protected or package-private or package-protected)
  • + for least-restricted or (public)

A good case can be made for + and - ... not sure about others.

Implicit encapsulation

The other approach is to implement information hiding simply by the position of entity declarations. This is normally done by nesting, for example, local variables are almost always automatically private to a function (or method or procedure) body:

function f(x) {
    var y;
    ...
}

Parameters are usually private to a function too. We say "usually" because in languages that support named parameter association, calling code can see the parameter name, but it can only be used in the call, so it's plenty safe.

We can have variables that are local to a block, or an iteration statement:

for i in x..y
  # Some code using i
end
x.upto(y) do |i|
  # Some code using i
end

One interesting style is to have a module in which there is one section (usually called the interface) which holds the visible identifiers and another section (the implementation) holding private stuff. A sketch:

module Stacks
    type Stack(int capacity);
    vpid push(Object)
    Object pop()
    int size()
implementation
    Any variable defined here is private
    to this entire implementation section
    . . .
    Here we expand on the interface items
    type Stack(int capacity) is
        int top = 0; 
        Object[] data = Array(Object).new(capacity)
    end
    void push(Object x) 
        raise Overflow if top == capacity;
        data[top++] = x
    end
    Object pop()
        raise Underflow if top == 0;
        data[top--]
    end
    int size()
        top
    end
end  

Hybrid Approaches

We can also have modules in which everything is private (hidden) by default — and an explicit export is needed.

module m
    export a;    // but not b
    int a, b;
    . . .
end

In some cases modules are completely closed off and you need an explicit import also.

int x, y;
. . .
module m
    import x;    // but not y
    export a;    // but not b
    int a, b;
    . . .
end

2010-05-02

Reserved Words

Many languages reserve words for their own use, meaning that you, the programmer, cannot use these words for your own purposes. Reserved words are related to keywords which are words used for certain purposes by the language, but which you can also use as you wish.

What is the motivation for a language to have reserved words? Are reserved words a good thing or not? Is there such thing as different degrees of being reserved?

Why reserve words at all?

A language might want to reserve words to limit confusion. The following are legal statements in PL/1, a language which chose not to reserve IF, THEN, ELSE, DO, and similar keywords:

IF THEN THEN THEN = ELSE; ELSE ELSE = THEN;
IF IF THEN ELSE = IF; ELSE THEN = ELSE;
DO WHILE (WHILE = DO); END = WHILE + DO; END;

Would anyone really write code like that? Even if someone felt the need to abuse keywords like that, simply reserving them doesn't completely prevent programmers from writing confusing code in other ways. There's no stopping this:

int subtract(int x, int y) {
    return x + y;
}

Perhaps the real reason languages reserve words is to make things easier for the compiler, or to give the language authors an outlet in which to be funny. For example, the word goto is reserved in Java, even though it isn't used for anything. Of course, nothing prevents a Java programmer from using the word in package names, comments, and string literals. And, as Java is case-sensitive, there's always class Goto ... .

Why not reserve words?

There are a few reasons for not reserving words:

  • Programmers should have the freedom to choose their own identifiers. It's the compiler's job to figure out when words are used in a particular context.
  • It's annoying to programmers. There are thousands of Java programs in the world using variable and parameter names called klass, clazz, or c, because class is verboten. (Awesome hackers might even use clаss — haha, the third letter there is a Cyrillic small letter a, not a Latin one!)
  • As a language evolves, the addition of new reserved words will break old code.

Keywords versus symbols

Here are three alternative syntaxes for a certain statement:

if greater(x, y) and w then begin assign x plus 4 to z; print z; end;
if (x > y && w) {z = x + 4; print z}
(x > y && w ==> z = x + 4, !z)

The obvious things to notice are that too many keywords make code too verbose and readability goes down. Too few keywords gives you cryptic code. Most people understand + and * and /, but really, a ! for "print"? In fact, most symbols aren't obvious at first. Different languages use = differently. And what about these things: <=>. =~. %. ===, ^, *., #, ??, and who knows what else? Anyone use APL?

Symbols are sometimes preferred to keywords for another reason: if keywords are in a language you don't speak, they might be harder to learn than symbols. Programmers that know Spanish but not English may prefer 'y' to 'and' and 'mientras' to 'while'. This is one use for macros, I suppose. In C:

#define mientras while

Symbols as keywords

In ML, identifiers can be alphanumeric or symbolic. So +, <=*=> and ====> are all identifiers. You can define functions with these names. And you can define + to do subtraction. You can even do that in Ruby. Is this okay? The choices seem to be:

  • Allow symbolic identifiers, but treat some as reserved words so that no programmer can override such basic operators as +.
  • Allow symbolic identifiers but place no restrictions on them. After all, the reason languages allow "operator overloading" is to allow addition on vectors and other structured objects.
  • Disallow symbolic identifiers but permit operator overloading (for the fixed set of predefined symbolic operators).
  • Prohibit both symbolic identifiers and operator overloading.

How reserved is reserved?

When a language specification says that a word is reserved, it generally means one of two things:

  • The word cannot, under any circumstances, be used as a name for any programmer-defined entity (e.g., a variable, constant, function, type, object property name, method, function parameter, statement label, etc.)
  • The word can be used to name some programmer-defined entities, but its position in the source code text is restricted to simplify language processing (specifically, tokenization).

The former case may be stricter than necessary because quoting, for one thing, works pretty well for object properties (at least):

point["long"] = 118.3532;

You can't stop people from using reserved words in string literals, after all. Similar to quoting is escaping; for example, you would write something like :

var @while = 2;

The @ is not part of the variable name, it's just an escape character that tells the compiler the variable is really named 'while' but we're going to use it as an identifier and not as the beginning of a while statement.

The second case is interesting. JavaScript, for example, reserves the word "long" and while it allows

point["long"] = 118.3532;

it does not allow

point.long = 118.3532;

The probable reason for this is that it wants its lexical analyzer to be independent of context: for it to simply look that the above text and tokenize it into

    IDENTIFIER ("point")
    DOT
    KEYWORD_LONG
    ASSIGNMENT_OPERATOR
    NUMBER ("118.3532")

But is that really important in practice anymore? Lexical analyzers can easily choose a different meaning for a token if, say, the previous token is a dot! That would allow point.long. Now what about var point = {lat: 40, long: -110}? It would seem we'd have to allow the lexical analyzer to have access to the parser's state, but really, just wait until the semantic analysis phase and allow certain known keyword tokens to be just as good as identifiers when it comes to object property names.

2010-04-29

Object Construction

There are countless ways to build objects. Here are a few.

Classic Constructors

Many class-based object oriented languages have constructors that look suspiciously like methods. Unlike instance methods which operate on existing objects, though, these constructors bring new objects into existence, and generally use a special syntax (such as an operator called new) to distinguish their invocation from that of a method.
new Point("Pantages Theater", 34.1017, -118.3255, 
    "Hollywood", "Los Angeles", "CA", "us", "90028", 
    new LocalDate(1930, 6, 4), Status.ACTIVE)
If there are too many parameters, you can pass in a map (dictionary, associative array, hash), or your language might support named parameter association.

Setters

With setter methods, you first construct an object in which all of its fields are set to default values, then you customize the object by setting just those fields that differ from the defaults.
Point p = new Point();
p.setName("Pantages Theater");
p.setLatitude(34.1017);
p.setLongitude(-118.3255);
p.setNeighborhood("Hollywood");
p.setCity("Los Angeles");
p.setState("CA");
p.setCountry("us");
p.setPostalCode("90028");
p.setEstablished(new LocalDate(1930, 6, 4));
p.setStatus(Status.ACTIVE);
This approach solves the three problems above, but introduces a new problem: the object being constructed can't be immutable. How can you get around this?
  • Some languages allow fields to be marked "final" so that after the first set, they can't be set again.
  • In some languages, you can scope the setter methods so that only the parts of the code that are supposed to the construct the objects can see the setters. Since objects should be able to be constructed anywhere, this all but requires the programmer to factor out construction code into its module, which could be unwieldy. But there are ways to do it nicely in general; one way is the builder, described next.

Builders

Builder objects are common too. They have the three advantages of the setter approach (no need to supply non-default values, order doesn't matter, and reader knows what the arguments mean), while also allowing the newly constructed object to be immutable.
Point p = new PointBuilder()
    .name("Pantages Theater");
    .latitude(34.1017);
    .longitude(-118.3255);
    .neighborhood("Hollywood");
    .city("Los Angeles");
    .state("CA");    
    .country("us");
    .postalCode("90028");
    .established(new LocalDate(1930, 6, 4));
    .status(Status.ACTIVE)
    .build();

Factory Methods

A factory method is any regular method (or regular function) that creates and returns a new object. There's no special syntax here; all that is done is to call a constructor, builder, or other device inside the body of the factory method. In Java:

public class Card {
    private Suit suit;
    private Rank rank;
    private Card(Suit s; Rank r) {       // Constructor must be private
        suit = s;                        // to force all clients to use
        rank = r;                        // the factory method below
    }
    public static Card fromRankAndSuit(Rank r, Suit s) {
        return new Card(s, r);
    }
    . . .
}

Literals

In languages without classes, or when classes are not too important (say, when there is duck typing), object literals create new objects. Here's a JavaScript example. Fields are string literals, but we get to omit the quotes if the field name is a simple word that is not a reserved word:

{name: "Pantages Theater", lat: 34.1017, "long": -118.3255, 
    neighborhood: "Hollywood", "state or province": "CA",
    country: "us", "postal code": "90028", city: "Los Angeles", 
    established: new LocalDate("1930-06-04"), status: Status.ACTIVE)}

Object literals are also possible in languages with statically typed, closed classes. In Ada:

type Point is record
    X: Integer;
    Y: Integer;
end record;
. . .
var P: Point := Point'(6, 5);
var Q: Point := Point'(Y => 5, X => 6);

Construction in Prototypal Languages

Modern (ECMAScript 5-based) JavaScript has nice features for creating objects with a given prototype. I came up with this pattern:

/*
 * An immutable circle datatype.  Synopsis:
 *
 * var c = Circle.create(5, {x: 1, y: 4});
 * c.radius      => 5
 * c.center      => {x: 1, y: 4}
 * c.area()      => 25π
 * c.perimeter() => 10π
 */
var Circle = {
    prototype: {
        area: function () {return Math.PI * this.radius * this.radius;},
        perimeter: function () {return 2 * Math.PI * this.radius;}
    },

    create: function (r, c) {
        return Object.create(this.prototype, {
            center: {value: c},
            radius: {value: r}
        });
    }
};

The circles we create with Circle.create are immutable because we use JavaScript's default property descriptors for center and radius: they're not writable, not enumberable, we can't delete them, nor can we change these settings. The same isn't true for the Circle properties (prototype and create), nor for the prototype's own properties...is it worth using property descriptors on these too?

2010-04-17

Global Variables

The concept of a global variable seems pretty simple, especially to beginning programmers writing a single-file program in a block-structured language. But for languages with modules, or languages that support multithreading or multiprocessing, or with scripting languages embedded in other systems that expose "host" objects via script variables, things are not so clear.

Most programmers would warn that globals should be used sparingly, for various reasons:

  • Because they can be written to from anywhere, it's harder to tell what might be going on just by looking at local portions of code. Code is harder to debug.
  • Globals make multithreaded programming harder to reason about, and make race conditions more likely to pop up.
  • Parameters are almost always a more readable and understandable way to "share" data among routines.

How do we live with, or manage, global variables? What constructs can a language have to mitigate these problems?

Languages that Require Global Variables

There's an interesting distinction between languages that allow global variables and those that require them. If a language allows pieces of a program to be brought together from different physical components (such as files), but does not provide a programming language construct like a module or package, then global variables are basically required to share information. Even if you adopt a message-passing type of communication between functions in different files, without a nice module construct, those functions are referenced with global variables.

Modules

Many languages have modules for the express purpose of limiting the number of global variables and hence minimizing the number of name collisions. The simplest example is that of a math module, found in most modern languages. Instead of global variables for E, PI, sin, cos, tan, etc., these values are wrapped in a module construct (usually called Math), which is the only top-level name exposed to the rest of the code. Examples:

# Ruby-like
module Math
  def sin(x) ... end
  def cos(x) ... end
  PI = 3.141592653589793
  E = 2.718281828459045
end
// JavaScript-like
var Math = {
    sin: function (x) {...},
    cos: function (x) {...},
    PI: 3.141592653589793,
    E: 2.718281828459045
};
# Java-like
public class Math {
    private Math() {}
    public static double sin(double x) {...}
    public static double cos(double x) {...}
    public static double PI = 3.141592653589793;
    public static double E = 2.718281828459045;
}

Modules create a namespace for these values which would otherwise be global. If there is a chance of having too many modules (that is, a possibility of having names of modules collide), modules can be grouped into some higher level named collection (Java calls this a package). Whether or not the additional construct is used, one can always use a hierarchical naming convention for global entities, starting, for instance, with a (reversed) DNS name that the programmer "owns."

Multithreading

The dangers of unprotected global variables in multithreading code (e.g., race conditions, lost updates) are so well known we don't need to explain them here. If you are stuck with a global, shared, variable for communication between threads, your language might provide some mechanism for atomic updating. For example:

atomic var balance = 0;

or

AtomicInteger balance = new AtomicInteger(0);

Internet Explorer Events

In most event-driven systems, an event object is passed to event handlers. If you are using JavaScript, and are writing event handlers to function on any browser except Internet Explorer, this will be the case. You write code like:

document.body.onclick = function (e) {
    alert("Clicked at (" + e.clientX + "," + e.clientY + ")");
}

With Internet Explorer, the event object is not passed to your handler; instead, the most recently fired event is accessed by a global variable (no kidding!) called event. IE gets away with this because client-side JavaScript is single-threaded: all events are queued and are handled sequentially. To make your code work on multiple browsers you can use the following idiom:

document.body.onclick = function (e) {
    if (!e) e = event;
    alert("Clicked at (" + e.clientX + "," + e.clientY + ")");
}

Sigils

Because local variables are usually better than global variables, one interesting design choice is to make locals the default and make globals ugly. Ruby does exactly this: global variables begin with a $ character. That's a sigil — a character used within a variable name to indicate its type, category, or (in this case) scope.

Example:
$x = 10
def f
  x = 3
  puts x
  puts $x
end
def g
  puts $x
end
def h
  puts x
end
f        # writes 3 then 10
g        # writes 10
puts $x  # writes 10
h        # raises a NameError

Another example:

x = 5
def f
  puts x
end
f        # raises a NameError

Hiding in Closures and Anonymous Functions

TODO

2010-03-13

Lambdas

Lambda-expressions, or anonymous functions, are common in many languages, but are either missing or approximated in others.

Simple Expressions

There are many ways to write lambda expressions when the body is a single expression:

λ x . x + 1
{x -> x + 1}                 // Curly braces are common
[x -> x + 1]                 // Not so common, looks like an array
(x -> x + 1)                 // Let the -> operator imply function type
fn x => x + 1                // ML
lambda (x) x + 1
(lambda (x) (+ x 1))
sub {$0 + 1}                 // Perl
{$0 + 1}
{_ + 1}                      // Scala
λ x y . 2 * x + y
{x y -> 2 * x + y}
fn x y => 2 * x + y
fn (x,y) => 2 * x + y
lambda (x, y) 2 * x + y
sub {2 * $0 + $1}
{2 * $0 + $1}

Some of these require a bit more lookahead to parse than others.

Complex Function Bodies

If your language has a sequencing expression, like C's comma expression, where e1, e2, e3 means to evaluate each expression in order and return the value of the last expression encountered, then you can use the sequencing expression in any of the forms above. Operator precedence becomes the only real issue, but parentheses can make it clear exactly what the function is.

{ p, i -> k = p * 0.45359237, m = 0.0254, k / (m * m) }

Let-expressions work well here, too

{ p, i -> let k = p * 0.45359237 and m = 0.0254 in k / (m * m) end }

Lambdas can be arbitrarily complex, with return statements. Some languages allow you to omit the return statement if the expression to return is the last one in the sequence.

TODO

Recursion

To arrange for an anonymous function to be called recursively, it needs to have a name or the language should reserve a special keyword to refer to the currently executing function (watch for scoping rules here).

{[f] n -> n <= 1 ? 1 : f(n - 1) * n}
{n -> n <= 1 ? 1 : CALLEE(n - 1) * n}

Allowing recursion in lambda expressions is far better than requiring the applicative Y combinator.

Closures

Lambdas often refer to variables in outer scopes. Within the lambda expression, these outside variables are called free variables.

function incrementer(int start, int delta) {
    var current = start - delta;
    return function () {return current += delta;}
}

Calling Lambda Expressions

Calling, or applying a function, is normally done with juxtaposition, though again precedence rules will often come into play.

(x -> x + 1)7
(x -> x + 1)(7)
[x -> x + 1](7 * y - 2)
[x -> x + 1] 7 * y - 2         // application or multiplication first? 
fn (x, y) => 2 * x + y (7, y)  // too confusing 
(fn (x, y) => 2 * x + y)(7, y)   

Currying

Sketches:
[x -> [y -> 2 * x + y]]
[x -> y -> 2 * x + y]
[x y -> 2 * x + y]
fn x => fn y => 2 * x + y
fn x y => 2 * x + y

Fake Lambdas

TODO

Delegates

TODO

2010-03-03

Prototypes

There are two primary ways that languages allow you to create a set of objects with the same (or similar) structure and behavior. In the classical approach, you define classes and then create objects from constructors associated with the class; in this case, objects are instances of the class. In the prototypal approach, you create a prototype object, and then instantiate new objects based on the prototype. Generally, a language is either classical (e.g., Java, Ruby, C#), or prototypal (e.g, JavaScript, Self, Io, Lua), though some languages let you construct objects both ways (e.g., ActionScript, Falcon).

What might prototype-based instantiations look like?

Simple Differential Inheritance

Perhaps the purest approach to a prototypal mechanism is one in which every object has an implicit link to another object, called its prototype. Whenever we look up a property in an object and it is not present, we go look in its prototype. If the property isn't present in the prototype, we search the prototype's prototype, and so on. (Writing a property is different, however; if the property doesn't exist in the object it is created right there.) Such a language might have an operator called beget which might be used like this:

var protoCircle = {x: 0, y: 0, radius: 1, color: "black"};
var c1 = beget protoCircle;
c1.x = 4;
c1.color = "green";

Here we have c1.x == 4, c1.y == 0, c1.radius == 1, and c1.color == "green".

We can create more circles:

var c2 = beget protoCircle;
c2.x = 4;
c2.radius = 15;
c3 = beget protoCircle;
which gives us this:

If we change any of the fields in the prototype, this change is picked up at run time by all the derived objects that haven't overridden those fields. Ditto for adding new fields to the prototype. To some people, this is convenient and flexible; to others it is ugly and error-prone. It's all those things, of course.

The prototype is also a great place to store function properties:

protoCircle.area = function () {return π * (this.radius ** 2);}

Here we've assumed we have a "this" operator which refers to the object through which the function was called (not necessarily the one along the prototype chain which ultimately contained the function).

Direct Cloning

Another approach is to define a prototype with default field values then clone it to make new objects. Cloning is different from simple differential inheritance because with cloning the new object automatically gets copy of all of the fields in the prototype, even for those that you wanted to keep the default values in the prototype. A clone operator might look like this:

var protoCircle = {x: 0, y: 0, radius: 1, color: "black"};
var c1 = clone protoCircle;
c1.x = 4;
c1.radius = 8;
c1.color = "green";

Cloning means c1 is going to get all four fields:

Cloning via user-defined functions

If a language does not have a built-in clone operator, or you just don't like the look of creating an object and then doing multiple assignments to override defaults, you can do the cloning and field assignments in a function. Default fields can be nicely managed with default parameters, in languages that have them:

function newCircle(x = 0, y = 0, r = 1, c = "black") {
    return {x: x, y: y, radius: r, color: c};
}
var c1 = newCircle(x => 4, r => 8, color => "green");
var c2 = newCircle(color => "yellow", r => 5);
var c3 = newCircle(_, 5, _, "blue"); 

or with a short circuit disjunction if you have that but no default parameters:

function newCircle(x, y, r, c) {
    return {x: x || 0, y: y || 0, radius: r || 1, color: c || "black"};
}
var c1 = newCircle(x => 4, r => 8, color => "green");

With cloning, we have the problem of where to put the objects' methods. How about global variables?

function circleArea(c) {return π * c.radius ** 2;}
function circlePerimeter(c) {return 2 * π * c.radius;}

That's awful! It pollutes the global namespace. What about putting them inside the objects?

function newCircle(x = 0, y = 0, r = 1, c = "black") {
    return {
        x: x, y: y, radius: r, color: c,
        area: function () {return π * this.radius ** 2;}
        perimeter: function () {return 2 * π * this.radius;}
    };
}

That's no good either — every time a circle object is created, two additional function objects are created for its area and perimeter. If we create thousands of circles we end up with thousands of identical area functions and thousands of perimeter functions sucking up memory. We should make sure we have only one copy of each (without defining global variables to access them). We want that nice little implicit link to the prototype back.

JavaScript Constructors

In JavaScript, prefixing a function call with new calls the function in a context in which the this expression refers to a newly constructed object, and, unless a return statement explicitly returns some other object, returns this newly constructed object.

function Circle(x, y, r, c) {
    this.x = x || 0;
    this.y = y || 0;
    this.radius = r || 1;
    this.color = c || "black";
}

It's also the case that JavaScript is prototypal, and weirdly so: every function is itself an object, with a property called prototype, whose value is the object that will be used as the prototype of every object created with that function. As usual, the prototype is the place where you drop in shared properties, like functions. Here's an example:

function Circle(x, y, r, c) {
    this.x = x || 0;
    this.y = y || 0;
    this.radius = r || 1;
    this.color = c || "black";
}
Circle.prototype.area = function () {return Math.PI * this.radius * this.radius;}
Circle.prototype.perimiter = function () {return Math.PI * 2 * this.radius;}
var c1 = new Circle(3, 8, 4, "green");
var c2 - new Circle(1, 7);
var c3 = new Circle();

Better Prototypal Patterns for JavaScript

It's pretty clear that JavaScript's new operator and the associated semantics for construction were designed to make the langusge look more classical. Douglas Crockford characterizes this beautifully by saying that "JavaScript is conflicted about its prototypal nature." He shows how to make JavaScript implement simple differential inheritance:

if (typeof Object.beget !== 'function') {
    Object.beget = function(o) {
        var F = function () {};
        F.prototype = o;
        return new F();
    };
}

Our running circle example can now be written like this in JavaScript:

var protoCircle = {x: 0, y: 0, radius: 1, color: "black"};
var c1 = Object.beget(protoCircle);
c1.x = 4;
c1.color = "green";

One of the nice things about using beget is we can hide away JavaScript's crazy new operator and never have to use it again. This operator is fairly confusing and error-prone. For example, when you call functions that are supposed to be called with new but aren't, the code ends up creating or overwriting global variables. Object.beget is a nicer approach.

ECMAScript 5 Improvements to JavaScript

Current JavaScript versions (as of mid-2010) are based on the 3rd Edition of ECMAScript, known as ECMAScript 3. The newly standardized ECMAScript 5 adds many properties to the Object object, including create, which is like the beget example above. In new JavaScript:

var protoCircle = {x: 0, y: 0, radius: 1, color: "black"};
var c1 = Object.create(protoCircle, {
    x: {value: 4}, 
    color: {value: "green"}
});

Much better.