04_data.txt

:chap_num: 4
:prev_link: 03_functions
:next_link: 05_higher_order
:load_files: ["js/code/jaques_journal.js", "js/04_data.js"]

= Data Structures: Object and Array =

[quote, Charles Babbage, Passages from the Life of a Philosopher (1864)]
____
On two occasions I have been asked, ‘Pray, Mr. Babbage, if you put
into the machine wrong figures, will the right answers come out?’
[...] I am not able rightly to apprehend the kind of confusion of
ideas that could provoke such a question.
____

(((data)))Numbers, booleans, and strings are the bricks that data
structures are built from. But you can't make much of a house out of a
single brick. Objects allow us to group values—including other
objects—together, and thus build more complex structures.

The programs we have built so far have been seriously hampered by the
fact that they were only operating on simple data types. This chapter
will add a basic understanding of data structures to your toolkit. By
the end of it, you'll know enough programming to start writing
significant programs.

The chapter will work through a more or less realistic programming
example, introducing concepts as they apply to the problem at hand.
The example code will often build on functions and variables that were
introduced earlier in the text.

ifdef::tex_target[]

The online coding sandbox for the book (`eloquentjavascript.net/code`)
will automatically load the needed code when you are running a
specific example. If you decide to work through the examples in
another environment, be sure to start from the full code for this
chapter (`04_data.js`, available from the web site).

endif::tex_target[]

== The weresquirrel ==

Every now and then, usually between eight and ten in the evening,
Jaques finds himself transforming into a small furry rodent with a
bushy tail.

On the one hand, Jaques is quite glad that he doesn't have classical
lycanthropy. Turning into a squirrel tends to cause fewer problems than
turning into a wolf. Instead of having to worry about accidentally
eating the neighbor (_that_ would be awkward), he worries about being
eaten by the neighbor's cat. After two occasions where he woke up on a
precariously thin branch in the crown of an oak, naked and
disoriented, he has taken to locking the doors and windows of his room
at night, and putting a few walnuts on the floor to keep himself busy.

image::img/weresquirrel.svg[alt="The weresquirrel"]

That takes care of the cat and oak problems. But Jaques still suffers
from his condition. The irregular occurrences of the transformation
make him suspect that there might be some trigger that causes them to
happen. For a while, he believed that it only happened on days when he
had touched trees. So he stopped touching trees entirely, and even
avoided going near them. But the problem persisted anyway.

Switching to a more scientific approach, Jaques intends to start
keeping a daily log of the things he did that day, and whether he
ended up changing form. Using such data on his own life, he hopes to
be able to narrow down the conditions that trigger the transformations.

The first thing he does is to design a data structure to store this
information.

== Data sets ==

In order to work with a chunk of digital data, we'll first have to
find a way to represent it in our machine's memory. Say, as a very
simple example, that we want to represent a collection of numbers.

We could get creative with strings—strings can have any length, so you
can put a lot of data into them—and use `"2 3 5 7 11"` as our
representation. But that is awkward. You'd have to somehow extract the
digits and convert them back to a number to access them.

(((Array type)))((([] (array))))Fortunately, JavaScript provides a
data type specifically for storing sequences of values. It is called
_((array))_, and it is written as a list of values between square
brackets, separated by commas.

[source,javascript]
----
var listOfNumbers = [2, 3, 5, 7, 11];
console.log(listOfNumbers[1]);
// → 3
console.log(listOfNumbers[1 - 1]);
// → 2
----

((([] (subscript))))The notation for getting at the elements inside an
array also uses square brackets. A pair of square brackets immediately
after an expression, with an expression inside of them, will look up
the element in the left-hand expression that corresponds to the index
given by the expression in the brackets.

These indices start at zero, not one. So the first element can be read
with `listOfNumbers[0]`. If you don't have a programming background
this might take some getting used to. Zero-based counting has a long
tradition in technology, and as long as that convention is
consistently followed (which it is, in JavaScript), it works very
well.

== Properties ==

(((property)))(((length property)))(((object,property)))We've seen a
few suspicious-looking expressions like `myString.length` (to get the
length of a string) and `Math.max` (the maximum function) in past
examples. These access _properties_ of another value. In the first
case, the `length` property of the value in `myString`. In the second,
the property named `max` in the `Math` object (which is a collection
of mathematics-related values and functions).

(((null value)))(((undefined value)))Almost all JavaScript values have
properties. The exceptions are `null` and `undefined`. If you try to
access a property on one of these non-values, you get an error.

// test: no

[source,javascript]
----
null.length;
// → TypeError: Cannot read property 'length' of null
----

((([] (subscript))))Arrays also have a `length` property, holding the
amount of elements in the array. In fact, the elements in the array
are also accessed through properties. Both `value.index` and
`value[index]` access a property on `value`. The difference is in how
`index` is interpreted. When using a dot, the part after the dot
(which must be a valid variable name) directly names the property.
When using square brackets, the index is treated as an expression that
is _evaluated_ to get the property name. Whereas `value.index` fetches
the property named “index”, `value[index]` tries to get the value of
the variable named `index`, and uses that as the property name.

So if you know that the property you are interested in is called
“length”, you say `value.length`. If you want to extract the property
named by the value held in the variable `i`, you say `value[i]`. And
finally, if you want to access a property named “0” or “John Doe”
(property names can be any string), these are not valid variable
names, so you are forced to use square brackets, as in `value[0]` or
`value["John Doe"]`, even though you know the precise name of the
property in advance.

== Methods ==

(((method)))(((String type)))Both string and array objects contain, in
addition to the `length` property, a number of properties that refer
to function values.

[source,javascript]
----
var doh = "Doh";
console.log(typeof doh.toUpperCase);
// → function
console.log(doh.toUpperCase());
// → DOH
----

(((toUpperCase method)))(((toLowerCase method)))Every string has a
`toUpperCase` property. When called, it will return a copy of the
string, in which all letters have been converted to uppercase. There
is also `toLowerCase`. You can guess what that does.

Interestingly, even though the call to `toUpperCase` does not pass any
arguments, the function does somehow have access to the string
`"Doh"`, the value of which it is a property. How this works precisely
is described in Chapter 6.

Properties that contain functions are generally called _methods_ of
the value they belong to. As in “`toUpperCase` is a method of a
string”.

This example demonstrates some methods that array objects have:

[source,javascript]
----
var mack = [];
mack.push("Mack");
mack.push("the", "Knife");
console.log(mack);
// → ["Mack", "the", "Knife"]
console.log(mack.join(" "));
// → Mack the Knife
console.log(mack.pop());
// → Knife
console.log(mack);
// → ["Mack", "the"]
----

(((Array type)))(((array,methods)))(((push method)))(((pop
method)))(((join method)))The `push` method can be used to add values
to the end of an array. The `pop` method does the opposite. It removes
the value at the end of the array and returns it. An array of strings
can be flattened to a single string with the `join` method. The
argument given to `join` determines the text that is glued between the
array's elements.

== Objects ==

Back to the weresquirrel. A set of daily log entries can be
represented as an array. But the entries do not consist of just a
number or a string—each entry needs to store a list of activities, and
a boolean value that indicates whether Jaques turned into a squirrel.
A practical representation needs to group these values together into a
single value, and then put such grouped values into the array of
entries.

(((Object type)))Values of the type _((object))_ are arbitrary
collections of properties, that we can add properties to (and remove
properties from) as we please. One way to create an object is by using
a curly brace notation:

[source,javascript]
----
var day1 = {
  squirrel: false,
  events: ["work", "touched tree", "pizza", "running",
           "television"]
};
console.log(day1.squirrel);
// → false
console.log(day1.wolf);
// → undefined
day1.wolf = false;
console.log(day1.wolf);
// → false
----

Inside of the curly braces we can give a list of properties, written
as a name followed by a colon and an expression that provides a value
for the property. Spaces and line breaks are again not significant.
When an object spans multiple lines, indenting it like we've been
indenting blocks of code helps readability. Properties whose names are
not valid variable names or valid numbers have to be quoted.

[source,javascript]
----
var descriptions = {
  work: "Went to work",
  "touched tree": "Touched a tree"
};
----

(((undefined value)))(((property,assignment)))(((mutability)))(((=
operator)))It is possible to assign a value to a property expression
with the ‘=’ operator. This will replace the property's value if it
already existed, or create a new property on the object if it didn't.

Reading a property that doesn't exist will produce the value
`undefined`.

To briefly come back to our tentacle model of variable
bindings—property bindings are similar. They _grasp_ values, but other
variables and properties might be holding on to the same values. So
now you may start thinking of objects as octopuses with any number of
tentacles, each of which has a name inscribed on it.

image::img/octopus-object.jpg[alt="Artist's representation of an object"]

(((delete operator)))(((property,deletion)))To cut off such a
leg—removing a property from an object—the `delete` operator can be
used. This is a unary operator that, when applied to a property access
expression, will remove the named property from the object. (Which is
not a very common thing to do in practice, but it is allowed.)

[source,javascript]
----
var anObject = {left: 1, right: 2};
console.log(anObject.left);
// → 1
delete anObject.left;
console.log(anObject.left);
// → undefined
console.log("left" in anObject);
// → false
console.log("right" in anObject);
// → true
----

The binary `in` operator, when applied to a string and an object,
returns a boolean value that indicates whether that object has that
property. The difference between setting a property to `undefined` and
actually deleting it is that, in the first case, the object still has
the property (it just doesn't have a very interesting value), whereas
in the second case the property is no longer present and `in` will
return `false`.

(((array)))Arrays, then, are just a kind of objects specialized for
storing sequences of things. If you evaluate `typeof [1, 2]`, this
produces `"object"`. I guess you can see them as long, flat octopuses
with all their arms in a neat row, labeled with numbers.

image::img/octopus-array.jpg[alt="Artist's representation of an array"]

The desired representation of Jaques’ journal is thus an array of
objects.

[source,javascript]
----
var journal = [
  {events: ["work", "touched tree", "pizza",
            "running", "television"],
   squirrel: false},
  {events: ["work", "ice cream", "cauliflower",
            "lasagna", "touched tree", "brushed teeth"],
   squirrel: false},
  {events: ["weekend", "cycling", "break",
            "peanuts", "beer"],
   squirrel: true},
  /* and so on... */
];
----

== Mutability ==

We will get to actual programming _real soon now_, I promise. But
first, a little more theory.

(((mutability)))(((side effect)))We've seen that object values can be
modified. The types of values discussed in earlier chapters are all
__immutable__—it is impossible to change an existing value of those
types. You can combine them and derive new values from them, but when
you take a specific string value, that value will always remain the
same. The text inside it cannot be changed. With objects, on the other
hand, the content of a value _can_ be modified by changing its
properties.

(((object,identity)))When we have two numbers, 120 and 120, they
can, whether they refer to the same physical bits or not, be
considered the precise same number. With objects, there is a
difference between having two references to the same object and having
two different objects that contain the same properties. Consider the
following code:

[source,javascript]
----
var object1 = {value: 10};
var object2 = object1;
var object3 = {value: 10};

console.log(object1 == object2);
// → true
console.log(object1 == object3);
// → false

object1.value = 15;
console.log(object2.value);
// → 15
console.log(object3.value);
// → 10
----

`object1` and `object2` are two variables grasping the _same_ value.
There is only one actual object, which is why changing `object1` also
changes the value of `object2`. The variable `object3` points to
another object, which initially contains the same properties as
`object1` but lives a separate life.

(((== operator)))JavaScript's `==` operator, when comparing objects,
will return `true` only if both values given to it are the precise
same value. Comparing different object with identical contents will
give `false`. There is no “deep” comparison operation built into
JavaScript, but it is possible to write it yourself.

== The lycanthrope's log ==

So Jaques starts up his JavaScript interpreter, and sets up the
environment he needs to keep his journal.

// include_code

[source,javascript]
----
var journal = [];

function addEntry(events, didITurnIntoASquirrel) {
  journal.push({
    events: events,
    squirrel: didITurnIntoASquirrel
  });
}
----

And then, every evening at ten—or sometimes the next morning, after
climbing down from the top shelf of his bookcase—the day is recorded.

[source,javascript]
----
addEntry(["work", "touched tree", "pizza", "running",
          "television"], false);
addEntry(["work", "ice cream", "cauliflower", "lasagna",
          "touched tree", "brushed teeth"], false);
addEntry(["weekend", "cycling", "break", "peanuts",
          "beer"], true);
----

Once he has enough data points, he intends to compute the correlation
between the squirrelification and each of the day events he recorded,
and hopefully learn something useful from those correlations.

Correlation is a measure of dependence between variables (“variables”
in the statistical sense, not the JavaScript sense). It is usually
expressed in a coefficient that ranges from -1 to 1. Zero correlation
means the variables are not related, whereas a correlation of one
indicates that the two are perfectly related—if you know one, you also
know the other. Minus one also means that the variables are perfectly
related, but that they are opposite to each other—when one of them is
true, the other is false.

(((phi coefficient)))For binary (boolean) variables, the phi
coefficient provides a good measure of correlation, and is relatively
easy to compute. First we need a matrix _n_, which indicates the
number of times the various combinations of the two variables were
observed. For example, we could take the event of eating pizza, and
put that in a table like this:

image::img/pizza-squirrel.svg[alt="Eating pizza versus turning into a squirrel"]

From such a table (n), the phi coefficient (ϕ) can be computed by the
following formula.

ifdef::html_target[]

++++
<style>sub { font-size: 60%; }</style>
<table style="border-collapse: collapse; margin-left: 1em;"><tr>
  <td>ϕ =&nbsp;</td>
  <td>
    <div style="border-bottom: 1px solid black; padding: 0 7px;">n<sub>11</sub>n<sub>00</sub> - n<sub>10</sub>n<sub>01</sub></div>
    <div style="padding: 0 7px;">√<span style="border-top: 1px solid black; position: relative; top: 2px;">
      <span style="position: relative; top: -4px">n<sub>1•</sub>n<sub>0•</sub>n<sub>•1</sub>n<sub>•0</sub></span>
    </span></div>
  </td>
</tr></table>
++++

endif::html_target[]

ifdef::tex_target[]

latexmath:[\phi = \frac{n_{11}n_{00}-n_{10}n_{01}}{\sqrt{n_{1\bullet}n_{0\bullet}n_{\bullet1}n_{\bullet0}}}]

endif::tex_target[]

Where n~01~ indicates the number of measurements where the first
measurement (pizza) is false (0), and the second (squirrelness) is
true (1), so 4 in this case. n~1•~ refers to the sum of all
measurements where the first variable is true, which is 10 in the
above table.

So for the pizza table, the part above the division line (dividend)
would be 1×76 - 9×4 = 40, and the part below it (divisor) would be the
square root of 10×80×5×85 = √340000. The actual coefficient then
becomes about 0.069, which is tiny, and thus likely to be random
noise. Eating pizza does not appear to have influence on the
transformations.

== Computing correlation ==

We can represent a two-by-two table with a four-element array (`[76,
9, 4, 1]`). Other representations are possible, such as an array
containing two two-element arrays (`[[76, 9], [4, 1]]`), or an object
with property names like `"11"` and `"01"`, but the flat array is
straightforward enough, and makes the expressions that access the
table pleasantly short. We'll interpret the indices to the array as
two-bit binary numbers, where the 1 component (the second digit)
refers to event variable, and the 2 component (the first digit) refers
to the squirrel variable. I.e. 2 is written in binary as 10, meaning
it refers to the field where the event (say, pizza) is true, but
Jaques did not turn into a squirrel.

(((phi coefficient)))This is the function that computes a phi
coefficient from such an array:

// test: clip
// include_code strip_log

[source,javascript]
----
function phi(table) {
  return (table[3] * table[0] - table[2] * table[1]) /
    Math.sqrt((table[2] + table[3]) *
              (table[0] + table[1]) *
              (table[1] + table[3]) *
              (table[0] + table[2]));
}

console.log(phi([76, 9, 4, 1]));
// → 0.068599434
----

(((square root)))(((sqrt function)))This is simply a less elegant
notation for the phi formula. `Math.sqrt` is the square root function,
as provided by the `Math` object in a standard JavaScript environment.
We have to sum two fields from the table to get fields like n~1•~,
because the sums of rows or columns are not stored directly in our
data structure.

Jaques kept his journal for three months. The resulting data set is
available in the coding sandbox for this chapter!!tex  (`eloquentjavascript.net/code`)!!,
where it is stored
in the `JOURNAL` variable, as well as in a downloadable
http://eloquentjavascript.net/code/jaques_journal.js[file].

To extract a two-by-two table for a specific event from this journal,
we must loop over all the entries and tally the frequencies with which
the event occurs in relation to squirrel transformations.

// include_code strip_log

[source,javascript]
----
function hasEvent(event, entry) {
  return entry.events.indexOf(event) != -1;
}

function tableFor(event, journal) {
  var table = [0, 0, 0, 0];
  for (var i = 0; i < journal.length; i++) {
    var entry = journal[i], index = 0;
    if (hasEvent(event, entry)) index += 1;
    if (entry.squirrel) index += 2;
    table[index] += 1;
  }
  return table;
}

console.log(tableFor("pizza", JOURNAL));
// → [76, 9, 4, 1]
----

The `hasEvent` function makes it easier (and more readable) to test
whether an entry contains a given event. Arrays have an `indexOf`
method that tries to find the given value (in this case, the event
name) in the array, and returns the index at which it was found—or -1
when it was not found. So testing whether result of the call `indexOf`
is not -1 will only produce true when the event is found in this
entry.

The body of the loop in `tableFor` figures out in which of the four
boxes this entry falls by adding 1 and 2 to an index variable
depending on whether this entry contains the event it is interested in
and whether it corresponds to a squirrel incident. It then adds one to
the number in the table that corresponds to this box.

We now have the tools we need to compute individual correlations. The
only step remaining is to find a correlation for all the types of
events that were recorded, and see if anything stands out. But first,
another short theoretical interruption.

== Objects as maps ==

How do we store a set of correlations, each labeled with a string? We
could store them all in an array, using objects with `name` and
`value` properties. But that makes looking up the number for a given
event name somewhat cumbersome—you'd have to loop over the whole array
to find the object with the right name. Such a thing could be wrapped
in a function, but we would still be writing more code, and the
computer would be doing more work, than necessary.

The solution, obviously, is to use object properties named after the
event types. We can use the computed property access notation to
create and read the properties, and the `in` operator to test whether
a given property exists.

[source,javascript]
----
var ages = {};
function storeAge(name, age) {
  ages[name] = age;
}

storeAge("Larry", 58);
storeAge("Simon", 55);
console.log("Larry" in ages);
// → true
console.log(ages["Simon"]);
// → 55
----

There are a few potential problems with using objects like this, which
we will discuss in Chapter 6, but for the time being, we won't worry
about those.

(((for/in loop)))What if we want to find all the people whose ages we
have stored? The properties don't form a predictable series, like they
would in an array. JavaScript provides a loop construct specifically
for going over the properties of an object. It looks a little like a
normal `for` loop, but distinguishes itself by the use of the word
`in`.

[source,javascript]
----
for (var name in ages)
  console.log(name + " is " + ages[name] + " years old");
// → Larry is 58 years old
// → Simon is 55 years old
----

So if we create a big object whose properties are named by the events
they refer to, and hold the correlation coefficients for those events,
we can uses `for`/`in` loop to further inspect them.

== The final analysis ==

To find all the types of events that are present in the data set, we
simply process each entry in turn, and then loop over the events in
that entry. We keep an object `phis` that has correlation
coefficients for all the event types we have seen so far. Whenever we
run across a type that we didn't see before—that isn't in the
`phis` object yet—we compute its correlation and add it to the
object.

// test: clip
// include_code strip_log

[source,javascript]
----
function gatherCorrelations(journal) {
  var phis = {};
  for (var entry = 0; entry < journal.length; entry++) {
    var events = journal[entry].events;
    for (var i = 0; i < events.length; i++) {
      var event = events[i];
      if (!(event in phis))
        phis[event] = phi(tableFor(event, journal));
    }
  }
  return phis;
}

var correlations = gatherCorrelations(JOURNAL);
console.log(correlations.pizza);
// → 0.068599434
----

Let us see what came out.

// test: no

[source,javascript]
----
for (var event in correlations)
  console.log(event + ": " + correlations[event]);
// → carrot:   0.0140970969
// → exercise: 0.0685994341
// → weekend:  0.1371988681
// → bread:   -0.0757554019
// → pudding: -0.0648203724
// and so on...
----

Most correlations seem to lie close to zero. Eating carrots, bread, or
pudding apparently does not trigger squirrel-lycanthropy. It does seem
to occur somewhat more often on weekends. Let's filter the results to
only show correlations greater than 0.1 (or smaller than -0.1).

// test: no

[source,javascript]
----
for (var event in correlations) {
  var correlation = correlations[event];
  if (correlation > 0.1 || correlation < -0.1)
    console.log(event + ": " + correlation);
}
// → weekend:        0.1371988681
// → brushed teeth: -0.3805211953
// → candy:          0.1296407447
// → work:          -0.1371988681
// → spaghetti:      0.2425356250
// → reading:        0.1106828054
// → peanuts:        0.5902679812
----

A-ha! There are two factors whose correlation is clearly stronger than
the others. Eating peanuts has a strong positive effect on the chance
of turning into a squirrel, whereas brushing his teeth has a
significant negative effect.

Interesting. Let us try something.

[source,javascript]
----
for (var i = 0; i < JOURNAL.length; i++) {
  var entry = JOURNAL[i];
  if (hasEvent("peanuts", entry) &&
     !hasEvent("brushed teeth", entry))
    entry.events.push("peanut teeth");
}
console.log(phi(tableFor("peanut teeth", JOURNAL)));
// → 1
----

Well, that's unmistakable! The phenomenon occurs precisely then when
Jaques eats peanuts and fails to brush his teeth. If only he wasn't
such a slob about dental hygiene, he'd never even have noticed his
affliction.

Having found this result, Jaques simply stopped eating peanuts
altogether, and found that this completely put an end to his
transformations.

All was well for a while, but a few years later, he lost his job.
Things went downhill, and he was forced to take employment with a
circus, performing as _The Incredible Squirrelman_ by stuffing his
mouth with peanut butter before every show. One day, fed up with this
depressing, pitiful existence, Jaques failed to change back into his
human form, hopped through a crack in the circus tent, and vanished
into the forest. He has not been seen again.

== Further arrayology ==

(((array,methods)))(((Array type)))Before finishing up this chapter, I
want to introduce you to a few more object-related concepts. We'll
start by introducing some generally useful array methods.

(((push method)))(((pop method)))(((shift method)))(((unshift
method)))We saw `push` and `pop`, which add and remove elements at the
end of an array, earlier in this chapter. The corresponding methods
for adding and removing things to the start of an array are called
`unshift` and `shift`.

[source,javascript]
----
var todoList = [];
function rememberTo(task) {
  todoList.push(task);
}
function whatIsNext() {
  return todoList.shift();
}
function urgentlyRememberTo(task) {
  todoList.unshift(task);
}
----

The above program manages lists of tasks. You add tasks to its end by
calling `rememberTo("eat")`, and then when you are ready to do
something, you call `whatIsNext()` to get (and remove) the front item
on the list. The `urgentlyRememberTo` function also adds a task, but
it adds it to the front instead of the back of the list.

(((indexOf method)))(((lastIndexOf method)))The `indexOf` method has a
sibling called `lastIndexof`, which starts searching at the end of the
array instead of the front.

[source,javascript]
----
console.log([1, 2, 3, 2, 1].indexOf(2));
// → 1
console.log([1, 2, 3, 2, 1].lastIndexOf(2));
// → 3
----

Both `indexOf` and `lastIndexOf` take an optional second argument that
indicates where to start searching.

(((slice method)))Another very fundamental method is `slice`, which
takes a start and an end index, and returns an array that has only the
elements between those indices. The start index is inclusive, the end
index exclusive.

[source,javascript]
----
console.log([0, 1, 2, 3, 4].slice(2, 4));
// → [2, 3]
console.log([0, 1, 2, 3, 4].slice(2));
// → [2, 3, 4]
----

When the end index is not given, `slice` will take all of the elements
after the start index. Strings, by the way, also have a `slice`
method, which has a similar effect.

(((concat method)))To glue arrays together, similar to what the ‘+’
operator does for strings, their `concat` method can be used. This
example function takes an array and an index, and returns a new array
that is the input array, but with the element at the given index
missing.

[source,javascript]
----
function remove(array, index) {
  return array.slice(0, index)
    .concat(array.slice(index + 1));
}
console.log(remove([1, 2, 3, 4, 5], 2));
// → [1, 2, 4, 5]
----

== Strings and their properties ==

We can read properties like `length` and `toUpperCase` from string
values. But if you try to add a new property, it doesn't stick.

[source,javascript]
----
var myString = "Fido";
myString.myProperty = "value";
console.log(myString.myProperty);
// → undefined
----

Types like strings, numbers, and booleans are not objects, and though
the language doesn't complain if you set new properties on them, it
doesn't actually have any place to store those properties.

But these types do have some built-in properties. Every string value
has a number of methods. The most useful ones are probably `slice`
and `indexOf`, which resemble the array methods by the same name.

[source,javascript]
----
console.log("coconuts".slice(4, 7));
// → nut
console.log("coconut".indexOf("u"));
// → 5
----

One difference is that a string's `indexOf` can take a string
containing more than one character (element), whereas the
corresponding array method only looks for a single element.

[source,javascript]
----
console.log("one two three".indexOf("ee"));
// → 11
----

The `trim` method removes whitespace (spaces, newlines, tabs, and
similar) characters from the start and end of a string. To only trim
one side, the `trimLeft` and `trimRight` methods can be used.

[source,javascript]
----
console.log("  okay \n ".trim());
// → okay
console.log("|" + " a ".trimLeft() + "|");
// → |a |
----

We have already seen the string type's `length` property. Accessing
the individual characters in a string can be done with the `charAt`
method, but also by simply reading numeric properties, like you'd do
for an array.

[source,javascript]
----
var string = "abc";
console.log(string.length);
// → 3
console.log(string.charAt(0));
// → a
console.log(string[1]);
// → b
----

== The arguments object ==

(((arguments object)))(((length property)))Whenever a function is
called, a special “magic” variable named `arguments` is added to the
environment in which the function body runs. This variable refers to
an object that holds all of the arguments passed to the function.
Remember that in JavaScript you are allowed to pass more—or
less—arguments to a function than the amount of parameters the
function itself declares.

[source,javascript]
----
function noArguments() {}
noArguments(1, 2, 3); // This is okay
function threeArguments(a, b, c) {}
threeArguments(); // And so is this
----

The `arguments` object has a `length` property that tells us the
amount of arguments that were really passed to the function. It also
has a property for each argument, named 0, 1, 2, and so on.

(((array,methods)))(((pseudo array)))If that sounds a lot like an
array to you, you're right, it _is_ a lot like an array. But this
object, unfortunately, does not have any array methods (like `slice`
or `indexOf`), so it is a little harder to use than a real array.

[source,javascript]
----
function argumentCounter() {
  console.log("You gave me", arguments.length,
              "arguments.");
}
argumentCounter("Straw man", "Tautology", "Ad hominem");
// → You gave me 3 arguments.
----

(((console.log function)))(((variadic function)))Some functions can
take any number of arguments, like `console.log` does. These typically
loop over the values in their `arguments` object. They can be used to
create very pleasant interfaces. For example, the entries to Jaques’
journal were created with calls like this:

[source,javascript]
----
addEntry(["work", "touched tree", "pizza", "running",
          "television"], false);
----

Since he is going to be calling this function a lot, we could create a
slightly nicer alternative:

[source,javascript]
----
function addEntry(squirrel) {
  var entry = {events: [], squirrel: squirrel};
  for (var i = 1; i < arguments.length; i++)
    entry.events.push[arguments[i]];
  journal.push(entry);
}
addEntry(true, "work", "touched tree", "pizza",
         "running", "television");
----

This reads its first argument (`squirrel`) in the normal way, and then
goes over the rest of the arguments (the loop starts at index 1,
skipping the first) to gather them into an array.

== The Math object ==

(((Math object)))(((min function)))(((max function)))(((sqrt
function)))As we've seen, `Math` is a grab-bag of number-related
utility functions, such `Math.max` (maximum), `Math.min` (minimum),
and `Math.sqrt` (square root).

(((namespace)))(((namespace pollution)))In the case of `Math`, an
object is used simply as a container to group a bunch of related
functionality. There is only one math object, and it is almost never
useful as a value. Rather, it provides a _namespace_, so that all
these functions and values do not have to be global variables.

Having too many global variables “pollutes” the namespace. The more
names have been taken, the more likely you are to accidentally
overwrite the value of some variable. For example, it is not a far
shot to want to name something `max` in one of our programs.

Many languages will stop you, or at least warn you, when you are
defining a variable with a name that is already taken. JavaScript does
neither, so be careful.

(((trigonometry)))(((cos function)))(((sin function)))(((tan
function)))(((acos function)))(((asin function)))(((atan
function)))(((PI constant)))Back to the `Math` object. If you need to
do trigonometry, `Math` can help. It contains `cos` (cosine), `sin`
(sine), `tan` (tangent), `acos`, `asin`, and `atan` functions. The
number π (pi)—or at least the closest approximation that fits in a
JavaScript number—is available as `Math.PI` (there is an old
programming tradition of writing the names of constant values in all
caps).

// test: no

[source,javascript]
----
function randomPointOnCircle(radius) {
  var angle = Math.random() * 2 * Math.PI;
  return {x: radius * Math.cos(angle),
          y: radius * Math.sin(angle)};
}
console.log(randomPointOnCircle(2));
// → {x: 0.3667, y: 1.966}
----

If sines and cosines are not something you are very familiar with,
don't worry, this book won't go into any complicated math.

(((random function)))The example above uses `Math.random`. This is a
function that returns a new pseudo-random number between zero
(inclusive) and one (exclusive) every time you call it.

// test: no

[source,javascript]
----
console.log(Math.random());
// → 0.36993729369714856
console.log(Math.random());
// → 0.727367032552138
console.log(Math.random());
// → 0.40180766698904335
----

(((pseudo-random numbers)))(((random numbers)))Through computers are
deterministic machines—they always react in the same way to the input
they receive—it is possible to have them produce numbers that appear
random. To do this, the machine keeps a number (or a bunch of numbers)
that, every time a random number is asked for, it performs some
complicated deterministic computations on. It then returns a part of
the result of those computations, and also uses their outcome to
change its internal number, so that the next random number produced
will be different.

(((floor function)))If we want a whole random number instead of a
fractional one, we can use `Math.floor` on the result of
`Math.random`.

// test: no

[source,javascript]
----
console.log(Math.floor(Math.random() * 10));
// → 2
----

Multiplying the random number by ten gives us a number greater than or
equal to zero, and below ten. `Math.floor` rounds down to the nearest
whole number, so it will produce (with equal chance) any of the
numbers 0, 1, 2, up to 9.

(((ceil function)))(((round function))))There are also `Math.ceil`
(ceiling, rounding up to a whole number) and `Math.round` (to the
nearest whole number).

== The global object ==

The global scope also acts as an object. In browsers, this object is
stored in the `window` variable. All global variables act as
properties of this object.

// test: no

[source,javascript]
----
var myVar = 10;
console.log(window.hasOwnProperty("myVar"));
// → true
console.log(window.myVar);
// → 10
----

== Summary ==

Objects and arrays provide ways to group several values into a single
value. Conceptually, this allows us to put a bunch of related things
in a bag, and run around with the bag, instead of trying to wrap our
arms around all of the individual things and trying to hold on to
them.

Most values in JavaScript have properties (the exceptions being `null`
and `undefined`). Properties are accessed using `value.propName` or
`value["propName"]`. Objects tend to use names for their properties,
and store a more or less fixed set of them. Arrays, on the other hand,
usually contain varying amounts of conceptually identical values, and
use numbers (staring from 0) as the names of their properties.

There _are_ some named properties in arrays, such as `length` and a
number of methods. Methods are functions that live in properties and
(usually) act on the value they are a property of.

== Exercises ==

Congratulations. You now know enough JavaScript fundamentals to write
useful programs.

=== The sum of a range ===

The introduction of this book alluded to this program as a nice way to
compute the sum of a range of numbers:

// test: no

[source,javascript]
----
console.log(sum(range(1, 10)));
----

Write a `range` function that takes two arguments, `start` and `end`,
and returns an array containing all the numbers from `start` up to
(and including) `end`.

Next, write a `sum` function that takes an array of numbers, and
returns the sum of these numbers. Run the above program and see
whether it does indeed return 55.

As a bonus assignment, modify your `range` function to take an
_optional_ third argument that indicates the “step” value used to
build up the array. If not given, it moves by steps of one,
corresponding to the old behavior. The call `range(1, 10, 2)` should
return `[1, 3, 5, 7, 9]`. Make sure it also works with negative step
values—so that `range(5, 2, -1)` produces `[5, 4, 3, 2]`.

ifdef::html_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(sum(range(1, 10)));
// → 55
console.log(range(5, 2, -1));
// → [5, 4, 3, 2]
----
endif::html_target[]

!!solution!!

Building up an array is easiest done by first initializing a variable
to `[]` (a fresh, empty array), and then repeatedly calling its `push`
method to add a value. Don't forget to return it at the end of the
function.

Since the end boundary is _inclusive_, you'll need to use the ‘\<=’
operator rather than simply ‘<’ to check for the end of your loop.

To check whether an optional argument was given, either check
`arguments.length` or compare the value of the argument to
`undefined`. If it wasn't given, simply set it to its default value
(1) at the top of the function.

Having `range` understand negative step values is probably best done
by writing two separate loops, one for counting up, and one for
counting down, because the comparison that checks whether the loop is
finished needs to be ‘>=’ rather than ‘\<=’ when counting downwards.

It might also be worthwhile to use a different default step, namely
-1, when the end of the range is smaller than the start. That way,
`range(5, 2)` returns something meaningful, rather than getting stuck
in an infinite loop.

!!solution!!

=== Reversing an array ===

(((reverse method)))Arrays have a method `reverse`, which will change
the array by inverting the order in which its elements appear. For
this exercise, write two functions, `reverseArray` and
`reverseArrayInPlace`. The first, `reverseArray`, takes an array as
argument and produces a _new_ array that has the same elements in the
inverse order. The second, `reverseArrayInPlace` does what the
`reverse` method does—it modifies the array given as argument in order
to reverse its elements.

Thinking back to the notes about side effects and pure functions in
the previous chapter, which variant do you expect to be useful in more
situations? Which one is more efficient?

ifdef::html_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(reverseArray(["A", "B", "C"]));
// → ["C", "B", "A"];
var arrayValue = [1, 2, 3, 4, 5];
reverseArrayInPlace(arrayValue);
console.log(arrayValue);
// → [5, 4, 3, 2, 1]
----
endif::html_target[]

!!solution!!

There are two obvious solutions to implementing `reverseArray`. The
first is to simply go over the array front-to-back and use the
`unshift` method on the new array to insert each element at its start.
The second is to loop over the input array backwards, and use the
`push` method. Iterating over an array backwards requires a (somewhat
awkward) `for` specification like `(var i = array.length - 1; i >= 0;
i--)`.

Reversing the array in place is harder. You have to be careful not to
overwrite elements that you will later need. Using `reverseArray` or
otherwise copying the whole array (`array.slice(0)` is a good way to
copy an array) works, but is cheating.

The trick is to _swap_ the first and the last element, and then the
one-but-first and one-but-last, and so on. You can do this by looping
over half the length of the array (use `Math.floor` to round down—you
don't need to touch the middle element in an array with an odd
length), and swapping the element at position `i` with the one at
position `array.length - 1 - i`. You can use a local variable to
briefly hold on to one of the elements, overwrite that one with its
mirror image, and then put the value from the local variable in the
place where the mirror image used to be.

!!solution!!

=== A list ===

(((list (data structure))))(((linked list)))Objects, by being generic
blobs of values, can be used to build all sorts of data structures. A
common data structure is the _list_ (not to be confused with the
array). A list is a set of objects, with the first object holding a
reference (in a property) to the second, the second to the third, and
so on.

// include_code

[source,javascript]
----
var list = {
  value: 1,
  rest: {
    value: 2,
    rest: {
      value: 3,
      rest: null
    }
  }
};
----

A nice thing about lists is that they can share parts of their
structure. For example, if I create two new values `{value: 0, rest:
list}` and `{value: -1, rest: list}` (with `list` referring to the
variable defined above), they are both independent lists, but they
share the structure that makes up their last three elements. In
addition, the original list is also still a valid three-element list.

Write a function `arrayToList` that builds up a data structure like
the one above when given `[1, 2, 3]` as argument, and a `listToArray`
function that produces an array from a list. Also write the helper
functions `prepend`, which takes an element and a list, and creates a
new list that adds the element to the front of the input list, and
`nth`, which takes a list and a number, and returns the element at the
given position in the list, or `undefined` when there is no such
element.

If you haven't already, also write a recursive version of `nth`.

ifdef::html_target[]

// test: no

[source,javascript]
----
// Your code here.

console.log(arrayToList([1, 2]));
// → {value: 1, rest: {value: 2, rest: null}}
console.log(listToArray(arrayToList([1, 2, 3])));
// → [1, 2, 3]
console.log(prepend(1, prepend(2, null)));
// → {value: 1, rest: {value: 2, rest: null}}
console.log(nth(arrayToList([1, 2, 3]), 1));
// → 2
----
endif::html_target[]

!!solution!!

Building up a list is best done back-to-front. So `arrayToList` could
iterate over the array backwards (see previous exercise), and for each
element, add an object to the list. You can use a local variable to
hold the part of the list that was built so far, and use a pattern
like `list = {value: X, rest: list}` to add an element.

To run over a list (in `listToArray` and `nth`), a `for` loop
specification like this can be used:

[source,javascript]
----
for (var node = list; node; node = node.rest) {}
----

Can you see how that works? The recursive version of `nth` will,
similarly, look at an ever smaller part of the “tail” of the list, and
at the same time count down the index until it reaches zero (at which
point it can return the `value` property of the node it is looking
at).

!!solution!!

=== Deep comparison ===

The ‘==’ operator compares objects by identity. Sometimes, you would
prefer to compare the values of their actual properties.

Write a function `deepEqual` that takes two values, and returns true
only if they are the same value, or objects with the same properties
whose values are equal, when compared with a recursive call to
`deepEqual`.

To find out whether to compare something by identity (use the ‘===’
operator for that) or by looking at its properties, you can test
whether applying the `typeof` operator on it produces `"object"`. But
you have to take one silly exception into account, because (through a
historical accident), `typeof null` also produces `"object"`.

ifdef::html_target[]

// test: no

[source,javascript]
----
// Your code here.

var obj = {here: {is: "an"}, object: 2};
console.log(deepEqual(obj, obj));
// → true
console.log(deepEqual(obj, {here: 1, object: 2}));
// → false
console.log(
  deepEqual(obj, {here: {is: "an"}, object: 2}));
// → true
----
endif::html_target[]

!!solution!!

Your test for whether you are dealing with a real object will look
something like `typeof x == "object" && x != null`. Be careful to only
compare properties when _both_ arguments are objects. In all other
cases you can simply immediately return the result of applying ‘===’.

Use a `for`/`in` loop to go over the properties. You need to both test
whether both objects have the same set of property names, and that
those properties have identical values. The first could be done by
counting the properties in both objects, ensuring that they have the
same amount, and then go over the properties of one object, and for
each of them, verify that the other object has the property. The
values of the properties are simply compared by a recursive call to
`deepEqual`.

Returning the right value from the function, when comparing
properties, is best done by immediately returning false when a
mismatch is noticed, and returning true at the end of the function,
which will (because `return` will jump out of the function) only be
reached when no mismatch was found.

!!solution!!