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What is happening under the hood in javascript when using the Array brackets notation

I have generally found javascript to be transparent, in that there are very few black boxes where "magic" just happens and you should just accept and look the other way, however I have not found any answer to how the Array brackets [] notation actually works under the hood.
let arr = [4, 5, 6, 7]
console.log(arr[3]) // <- How does this work?
What is javascript doing to access the item at index 3. Does it internally call some method on the Array.prototype?
With an object, the [] is a shortcut for a property accessor.
let obj = {
a: 'hello',
b: 'world'
}
obj['a'] === obj.a // true
Is an array then just an object with a long list of integer based properties?
let objArray = {
0: 'hello',
1: 'world'
}
let realArray = ['hello', 'world']
objArray[0] === 'hello' // true
realArray[0] === 'hello' // true
objArray.0 // SyntaxError: Unexpected number
realArray.0 // SyntaxError: Unexpected number
I have seen many many online discussions that all come to the conclusion that you cannot overload the brackets notation to truly subclass an Array but I have never seen an explanation on what magic is happening under the hood that allows the Array to work the way it does.
The obvious follow up question is whether there is any way to intercept the bracket notation access to define your own behavior, but I think I already know the answer to that.

You'd probably have to look at the implementation code to know precisely what's going on, but the basic idea is that arrays are actually layered atop objects.
This is backwards:
With an object, the [] is a shortcut for a property accessor.
The bracket notation is more fundamental. Thus, obj['foo'] and obj.foo work the same, but there is no equivalent for obj['foo & bar'], which is perfectly legitimate, and will respond with a value if obj has a key named "foo & bar".
Is an array then just an object with a long list of integer based properties?
Not quite, but you're not far off. Arrays are objects with the Array prototype, and with a little bit of additional magic to set the length property when new keys are added, or remove keys when that length is set.
And no, you cannot override the [] operator for your own purposes.

Is an array then just an object with a long list of integer based properties?
Yes, in it's simplest form, an Array is an Object with a list of integer base properties that is based on the Array prototype (which gives access to all the array methods like map, forEach, etc.)
As for intercepting the bracket notation, no, I have not seen anything that would allow that besides creating your own Object that has the methods you need (and then only access that object via the appropriate methods).
More info from MDN:
Arrays are list-like objects whose prototype has methods to perform traversal and mutation operations. Neither the length of a JavaScript array nor the types of its elements are fixed. Since an array's length can change at any time, and data can be stored at non-contiguous locations in the array, JavaScript arrays are not guaranteed to be dense; this depends on how the programmer chooses to use them. In general, these are convenient characteristics; but if these features are not desirable for your particular use, you might consider using typed arrays.
Arrays cannot use strings as element indexes (as in an associative array) but must use integers. Setting or accessing via non-integers using bracket notation (or dot notation) will not set or retrieve an element from the array list itself, but will set or access a variable associated with that array's object property collection. The array's object properties and list of array elements are separate, and the array's traversal and mutation operations cannot be applied to these named properties.
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Indexed_collections#Array_object

Creating multi-dimensional arrays in javascript, error in custom function

I was trying to define an array (including other arrays as values) in a single javascript statement, that I can loop through to validate a form on submission.
The function I wrote to (try to) create inline arrays follows:
function arr(){
var inc;
var tempa = new Array(Math.round(arguments.length/2));
for(inc=0; inc<arguments.length; inc=inc+2) {
tempa[arguments[inc]]=arguments[inc+1];
}
return tempa;
}
This is called three times here to assign an array:
window.validArr = arr(
'f-county',arr('maxlen',10, 'minlen',1),
'f-postcode',arr('maxlen',8, 'minlen',6)
);
However in the javascript debugger the variable is empty, and the arr() function is not returning anything. Does anyone know why my expectations on what this code should do are incorrect?
(I have worked out how to create the array without this function, but I'm curious why this code doesn't work (I thought I understood javascript better than this).)

Well from what your code does, you're not really making arrays. In JavaScript, the thing that makes arrays special is the management of the numerically indexed properties. Otherwise they're just objects, so they can have other properties too, but if you're not using arrays as arrays you might as well just use objects:
function arr(){
var inc;
var tempa = {};
for(inc=0; inc<arguments.length; inc=inc+2) {
tempa[arguments[inc]]=arguments[inc+1];
}
return tempa;
}
What you're seeing from the debugger is the result of it attempting to show you your array as a real array should be shown: that is, its numerically indexed properties. If you call your "arr()" function as is and then look at (from your example) the "f-county" property of the result, you'll see something there.
Also, if you do find yourself wanting a real array, there's absolutely no point in initializing them to a particular size. Just create a new array with []:
var tempa = [];

Your code works. Just inspect your variable, and you will see that the array has the custom keys on it. If not expanded, your debugger shows you just the (numerical) indixed values in short syntax - none for you.
But, you may need to understand the difference between Arrays and Objects. An Object is just key-value-pairs (you could call it a "map"), and its prototype. An Array is a special type of object. It has special prototype methods, a length functionality and a different approach: to store index-value-pairs (even though indexes are still keys). So, you shouldn't use an Array as an associative array.
Therefore, their literal syntax differs:
var array = ["indexed with key 0", "indexed with key 1", ...];
var object = {"custom":"keyed as 'custom'", "another":"string", ...};
// but you still can add keys to array objects:
array.custom = "keyed as 'custom'";

Is associative array element the same as an object field?

I have an object that looks something like this.
var obj = {
speed: 10,
volume: 14,
aux_deform: 1.8,
energy: 21.5,
aux_energy: 0.2
}
There will be additional fields/properties added at runtime, so the object can contain any number of properties at any given time. As you can see in my object example, some properties can start with "aux_".
Now, I want to create another object from this one that contains only properties that start with "aux_".
The way I am doing it now is something like this.
var newObj = [];
for(prop in obj)
{
if (prop.startsWith('aux_'))
{
newObj[prop] = obj[prop];
}
}
Now I have a new object and I can do something like:
alert(newObj.aux_energy);
This works ok, but I am wondering if this is the right approach. Is there any easier way, or a more elegant way for what I am trying to achieve? Are there any (security or technical) issues/problems with this way of creating objects?
And the question from the title: is the newly created object actually an associative array with properties as keys (since it's created that way) or is there any difference.

There are no associative arrays in Java Script, there are only JSON objects which can be used in place of associative arrays. What you did here is that you have declared an array called newObj and then added properties to this array. It could lead to unexpected behaviors when trying to use buit in Array methods or when iterating over it. The main difference between JSON objects and arrays is that properties in objects aren't sortable and iterating over them can produce random and unpredictable output.
More appropriate way to write that would be to declare an object newObj = {} and then just copy the properties you need.
One thing to note - if you will have arrays or objects as values for properties you will copy references to these objects. If you'd like to be able to edit these values independently from the original object you'd have to deep copy these values - check this question for how to on that What is the most efficient way to deep clone an object in JavaScript?
Apart from that it's the only way to do that and it's perfectly fine.

How do I access the first key of an ‘associative’ array in JavaScript?

I have a js 'associative' array, with
array['serial_number'] = 'value'
serial_number and value are strings.
e.g. array['20910930923'] = '20101102'
I sorted it by value, works fine.
Let's say I get back the object 'sorted';
Now I want to access the first KEY of the 'sorted' array.
How do I do it? I can't think I need an iteration with
for (var i in sorted)
and just stop after ther first one...
thanks
edit: just to clarify, I know that js does not support associative arrays (that's why I put it in high commas in the Title).

2021 Update
Since ES6, properties with string keys are enumerated in insertion order. Here's a nice summary. My original answer from 2010 was correct at the time and is preserved below:
Original answer
JavaScript object properties are specified to have no order, much though many people wish it were different. If you need ordering, abandon any attempt to use an object and use an Array instead, either to store name-value objects:
var nameValues = [
{name: '20910930923', value: '20101102'},
{name: 'foo', value: 'bar'}
];
... or as an ordered list of property names to use with your existing object:
var obj = {
'20910930923': '20101102',
'foo': 'bar'
};
var orderedPropertyNames = ['20910930923', 'foo'];

Try this:
// Some assoc list
var offers = {'x':{..some object...}, 'jjj':{...some other object ...}};
// First element (see attribution below)
return offers[Object.keys(offers)[0]];
// Last element (thanks to discussion on finding last element in associative array :)
return offers[Object.keys(offers)[Object.keys(offers).length - 1]];

Actually JavaScript doesn't support associative arrays, so you can't loop through it in an implied order (e.g. you can't access it via the indexer property array[0] won't access the first element in your object). The syntax is what makes it look like it does, but in reality it doesn't. So you have no "Order" to your objects.
http://www.hunlock.com/blogs/Mastering_Javascript_Arrays
Javascript does not have, and does not
support Associative Arrays. However…
All arrays in Javascript are objects
and Javascript's object syntax gives a
basic emulation of an associative
Array. For this reason the example
code above will actually work. Be
warned that this is not a real array
and it has real pitfals if you try to
use it. The 'person' element in the
example becomes part of the Array
object's properties and methods, just
like .length, .sort(), .splice(), and
all the other built-in properties and
methods.

Just thinking off the top of my head, but could you have another array with the key value pairs swapped?
So the answer would be arrayKeyValueReversed['20101102'] = '20910930923';
When you sort the array, use the first item (array[0]) as the key to get the value in the arrayKeyValueReversed.

In JavaScript, how do I access an object inherited from Array with the [] operator?

I have a situation, where I need to create a new JavaScript object that is inherited from Array. I am using the following code:
// Create constructor function.
var SpecialArray = function () {};
// Create intermediate function to create closure upon Array's prototype.
// This prevents littering of native Array's prototype.
var ISpecialArray = function () {};
ISpecialArray.prototype = Array.prototype;
SpecialArray.prototype = new ISpecialArray();
SpecialArray.prototype.constructor = SpecialArray;
// Use Array's push() method to add two elements to the prototype itself.
SpecialArray.prototype.push('pushed proto 0', 'pushed proto 1');
// Use [] operator to add item to 4th position
SpecialArray.prototype[4] = 'direct [] proto to 4';
// Create new instance of Special Array
var x = new SpecialArray();
// Directly add items to this new instance.
x.push('pushed directly on X');
x[9] = 'direct [] to 9'
console.log(x, 'length: ' + x.length);
Quite interestingly, the [] operation seem to be useless and the console output is:
["pushed proto 0", "pushed proto 1", "pushed directly on X"] length: 3
What am I missing here?

It is not possible to subclass the Array class and use t this way.
The best solution for you is to extend just the array class and use it as it is.
There are two other options that I do not like but they exist
http://ajaxian.com/archives/another-trick-to-allow-array-subclasses
http://dean.edwards.name/weblog/2006/11/hooray/

This is one of those that always trips people up. The length property only applies to the ordered elements. You can't extend an array then insert an arbitrary non-sequitous key and expect it to work. This is because the relationship between the length property and the array contents is broken once you extend the array. Pointy's link above does a very good job of explaining this in more detail.
To prove this add this to the end of your example:
console.log(x[4]);
As you can see your entry is present and correct, it's just not part of the ordered array.
Like everything else in javascript the Array object is just a Associative Array with string keys. Non numerical, non sequitous keys are hidden to fool you into thinking it's a 'proper' numerically indexed array.
This strange mixed design of the Array object does mean you can do some strange and wonderful things like storing ordered and unordered information in the same object. I'm not saying this is a good idea, I'm just saying it's possible.
As you will have noticed by now when iterating structures like this the non sequitous keys don't appear which makes sense for the general use case of arrays for ordered information. It's less useful, or in fact useless when you want to get keyed info. I would venture that if ordering is unimportant you should use an object not an array. If you need both ordered and unordered store an array as a property in an object.

The best way I have found to create a child prototype of an "Array" is to not make a child prototype of "Array" but rather create a child of an "Array-Like" prototype. There are many prototypes floating around that attempt to mimic the properties of an "Array" while still being able to "inherit" from it, the best one I've found is Collection because it preserves the ability to use brackets []. The major downfall is that it doesn't work well with non-numeric keys (i.e. myArray["foo"] = "bar") but if you're only using numeric keys it works great.
You can extend this prototype like this:
http://codepen.io/dustinpoissant/pen/AXbjxm?editors=0011
var MySubArray = function(){
Collection.apply(this, arguments);
this.myCustomMethod = function(){
console.log("The second item is "+this[1]);
};
};
MySubArray.prototype = Object.create(Collection.prototype);
var msa = new MySubArray("Hello", "World");
msa[2] = "Third Item";
console.log(msa);
msa.myCustomMethod();