Develop Reference

What is the difference between (function(){/*.....*/})(); and (function($){/*.....*/})(jQuery);

Is there difference between :
(function() {
/*..........*/
})();
and :
(function($) {
/*..........*/
})(jQuery);

Other people explained what the difference is, but not why you use the latter.
The $ variable is most often used by jQuery. If you have one script tag that loads jQuery and another that loads your code, it's perfectly fine. Now throw prototype.js into the mix. If you load prototype.js and then jQuery, $ will still be jQuery. Do it the other way around and now $ is prototype.js.
If you tried to use $ on such a page, you'd likely get errors or weird behavior.
There are many questions on StackOverflow about this problem. Plugins shouldn't assume much about the page they're loaded in, so they use this pattern defensively.

i am asking if there is difference between (function(){/…/})(); and (function($){/…/})(jQuery);
A little difference. In case of (function($){/*…*/})(jQuery); and absense of jQuery you'll get an error message immeditally after page loads. It's a simpler to detect jquery absense or incorrect order of scripts inclusion, when jquery-based code included before jQuery.
In case of (function(){/*…*/})(); you'll get an error message when code inside this construction actually call one of jQuery methods. It's harder to detect this error, but on the other side you can include your jquery-based scripts before jquery.
I prefer first case.

The second form, (function($){/*…*/})(jQuery); can be slightly safer when working in an environment where you don't (or can't) strictly enforce what code gets put on your site.
I used to work on a large site with a lot of third-party ads. These ads would often unsafely inject their own version of jQuery and occasionally they would override jQuery's global $ object. So, depending on how we wrote our code, we might be calling methods that no longer existed or had slightly different behaviour from what we expected. This could be impossible to debug, since some ads would never appear in our area or were excluded from our environment. This meant we had to be extremely protective of scope, inject our dependencies before any ad code had a chance to load, namespace anything that had to be global and pray no ad screwed with us.

Other answers are quite fragmented so I'd like to give a more detailed answer for the question.
The main question can be self-answered if you understand..
What does (function(argument){ /*...*/ })(value); mean?
It's a quick hand version of:
var tempFunction = function(argument){
/* ... */
}
tempFunction(value);
Without having to go through the hassle of conjuring up a new terrible name for a function that you will only call once and forget. Such functions are called anonymous functions since they aren't given a name.
So (function(){/*...*/})() is creating a function that accept no argument and execute it immediately, while (function($){/*...*/})(jQuery) is creating a function that accept one argument named $, and give it the value of jQuery.
Now that we know what the expression means, surely the first think on our mind is
"Why?". Isn't $ jQuery already?
Well, not exactly. We can never be sure. $ is an alias of jQuery, but other libraries can also use the same alias. As user #FakeRainBrigand already pointed out in his answer, prototype.js also use $ as its alias. In such cases, whichever library assigns its value to $ later wins out.
The practice of (function($){...})(jQuery) is very similar to an alias import in other programing languages. You are explicitly telling the system that your function:
Requires an object/library named jQuery, and
Within your function, $ means jQuery.
So even when someone include a new library later that override the alias $ at the global level, your plugin/framework still works as intended.
Because javascript is so... "flexible" in variable assignment, some people (including me) go as far as doing things like
var myApplication = (function($, undefined){ ... })(jQuery);
Apply the same understanding, it is easy to interpret the second argument part as: assign nothing to the variable undefined. So we can be sure that even if some idiot assigned a value to undefined later, our if(checkVariable === undefined){} won't break. (it's not a myth, people really do assign values to undefined)
When is it commonly used in javascript?
This anonymous function practice is most commonly found in the process of providing encapsulation for your plugin/library.
For example:
var jQuery = (function(){
var publicFunction = function(){ /* ... */}
var privateFunction = function(){ /* ... */}
return {
publicFunction : publicFunction
}
})();
With this, only jQuery.publicFunction() is exposed at the global scope, and privateFunction() remains private.
But of course, it is also used any time you simply want to create a function, call it immediately, and throw it away. (For example as a callback for an asynchronous function)
For the bonus question
why they used (function(){}() twice in the below code?
Well, most likely because they don't know what they're doing. I can't think of any reason to put nested function in like that. None at all.

(function(){/*...*/})(); does not set $ as reference to jQuery within IIFE and (function($){/*...*/})(jQuery); sets $ or other parameter name; e.g.; (function(Z){/*...* Z("body") where Z : jQuery*/})(jQuery); as reference to jQuery within IIFE

The they are both closures. The first is just an anonymous function that will fire any well formatted code that is inside immediately. The second is the jQuery closure. It is how the jQuery library initiates it wraps its code in the JQuery object and exposes it isn't the $ symbol.
(function(){}()) // this is a closure
(function($){}(jQuery)) // is a closure that wraps the executed code inside of the jQuery returned object and exposes it via the $.

With this (function(){/*…*/})();, you are not passing any argument to the inner function, while with this (function($){/*…*/})(jQuery); you are passing jQuery as argument to the inner function and expecting its value as $(which means, you will be able to use jQuery inside the inner function).
Ex:
(function($){
$(document).ready(function() {
console.log('all resources loaded');
})
})(jQuery);

They both are examples of Immediately Invoked Function Expression. In that sense, there is no difference between (function(){/*…*/})(); and (function($){/*…*/})(jQuery);. So no benefits are gained by wrapping (function($){/*…*/})(jQuery); inside (function(){/*…*/})();
A new execution context is created when a function is executed. So when (function(){/*…*/})(); is executed a context is created. Again when (function($){/*…*/})(jQuery); is executed, another context is created. Since the first context is not used (i.e. no variables are declared inside it), I don't see any advantages gained by the wrapping.
(function() { // <-- execution context which is not used
(function($) { // <-- another execution context
"use strict";
/*..........*/
})(jQuery);
})();

Way to execute jQuery member functions inside setTimeout without closure?

I was trying to do something along these lines:
setTimeout($('#element').hide,3000);
which seems simple enough, but it is crippled by the "this" problem. I want to find a way to just pass the actual function as a parameter, without wrapping it in another function, e.g. I do not want to do this:
setTimeout(function(){$('#element').hide();},3000);
What I've tried:
setTimeout($('#element').hide,3000);
setTimeout($('#element').hide.apply(document),3000); /* jQuery docs say that document is the default context */
setTimeout($('#element',document).hide,3000);
setTimeout($(document).find('#element').hide,3000);
setTimeout($(window).find('#element').hide,3000);
setTimeout($.proxy($('#element').hide,document),3000); /* I know this returns a function, which I don't want, but I have tried it */
setTimeout(($('#element').hide()),3000); /* functional expression */
I'm looking for the way to remedy this problem, but I don't want to wrap it in another function. The less lines of code, the better. I know WHY this isn't working as expected, but HOW can I fix it without wrapping it in a closure?

You can do this way by binding the context of the method with the element itself so that in jquery hide method this will point to jquery object and not global context. You can create bound functions using:
Function.bind
Cross Browser Alternative for this:
$.proxy
Ex:
var $elem = $('#element');
setTimeout($elem.hide.bind($elem),3000);
or
setTimeout($.proxy($elem.hide, $elem),3000);
or
setTimeout($.fn.hide.bind($elem),3000); //setTimeout($.proxy($.fn.hide, $elem),3000);
Fiddle

Executing dynamically passed function call with jQuery

I have this function call passed as a string:
var dcall = "tumbsNav(1)";
Is it possible to execute this dynamically like exec in SQL??
exec(dcall)

eval is the equivalent, but you should NOT use it.
Instead, pass the function like this:
var dcall = function() {tumbsNav(1);};
Then call it with:
dcall();

To do this, you want eval(dcall).
eval can open terribly security holes and performance issues in your program. If you need to use it, that usually means you have designed your program poorly.
Instead, you might keep a reference to the function you want to call and hold an array of arguments and use apply, e.g., tumbsNav.apply(null, [1]);. I don't know your code, so that's most general solution I can offer.

Wherever you're storing
var dcall = "tumbsNav(1)";
You can instead store
var dcall = function() {
return tumbsNav(1);
};
Wherever you were calling it, instead of calling
eval(dcall);
You can instead call
dcall();
The only case this wouldn't work is if tumbsNav wasn't defined at the time var func = ... is called. Then you would have to store the string. If the string is completely under your control, then there's no security hole, but be aware of all the problems mentioned by #Porco
As Kolink mentioned, my example would not cause a problem if tumbsNav was not defined when assigning it with a wrapped anonymous function that calls tumbs. The comment above would only make sense if the example had been the following:
var dcall = tumbsNav, darg = 1;
// later in the code, you can call
dcall(darg) ;

Use eval(dcall).
As others have mentioned eval is considered bad practice. The main reasons for this are
1) Improper use can leave your code vulnerable to injection attacks.
2) Maintaining code becomes more difficult (no line numbers, can't use debugging tools)
3) Executes more slowly (browsers can't compile)
4) Scope becomes impossible to predict.
However, if you understand all these then eval can be very helpful.

Best approach to avoid javascript's “this” mistakes in XBL

Talking about XBL is not exactly talking about javascript. So I'll create this question that's related to this one, but now about XBL, where I'm not the creator of the root javascript code, but just of the methods and event handlers inside the bindings.
--
In some cases, the this keyword may not refer to the object I expect it to. (recent example: in an key event, in my XBL)
What's the best approach to avoid this kind of mistake?
For now, I'm using always the getElementById (or $.fn from jQuery), but I'm not sure if it's the best approach.
--update
A little bit more details:
Within a XBL method the only way to access the element that was defined in the Xul file (the GUI description file) without using "this" (as it may not be the "this" I expect) is with getElementById, and this makes the code not reusable, so I'm looking for alternatives..

As you've heard elsewhere, the problem is that the this parameter isn't necessarily the object you first thought of, especially when you're talking about event handlers and the like. The best way I found is to write a small function that will bind some object as the this variable and return another function that uses the binding to call the original function.
Take a look at this code:
var bindFunction = function(self, f) {
return function() {
return f.apply(self);
};
};
var foo = function() {
alert(this.hello);
};
var bar = {
hello: "Hello there"
};
var boundFoo = bindFunction(bar, foo);
boundFoo();
What I have is a function called bindFunction that takes an object (called self) and some function, and returns another function that will call the passed-in function applying the self object as the this variable.
The rest of the code is just some test code: a foo function that will alert this.hello, a bar object with a hello member, and how you can bind foo with bar.
In essence, I've taken a function that accepts no parameters and generated another function that will ensure the first is always called with the correct this variable. Ideal for event handlers.
(Sorry, but I know nothing about XBL, so I hope this will be of use.)

If there's not a best answer, a good approach could be use javascript files instead of XBL for the implementation. Looking the Xulrunner source code, looks like most code does this.
But I still would like to use XBL, if there was a way to work fine with it..

JQuery\Javascript - Passing a function as a variable

I was just curious if I could pass a function as a variable. For example:
I have a function
$('#validate').makeFloat({x:671,y:70,limitY:700});
I would like to do something like this:
$('#validate').makeFloat({x:function(){ return $("#tabs").offset().left+$("#tabs").width();},y:70,limitY:700});
This does not work, but ideally every time the variable was accessed it would compute the new value. So if the window was resized it would automatically adjust as opposed to a variable passed in being static. I realize I can implement this directly inside the function\widget, but I was wondering if there was some way to do something like the above.
The concept of this is independent of the plugin. I am talking about the function being "cast" as a variable.

Yes, you can pass an object which will invoke some function when its property is read (this is called a getter), but it is not cross-browser compatible. For example, this will (probably) work in IE9:
var o = {y:70, limitY:700};
Object.defineProperty(o, 'x', {get: function() {return 671;}});
$('#validate').makeFloat(o);
There are other syntaxes for other browsers such as __defineGetter__ for Firefox, and some browsers don't have this functionality at all. So it is practically useless unless you can fully control the environment where your code runs.

This won't work unless x is invoked (obj.x(), instead of just obj.x).
To make it work, the makeFloat() code must check the type of x, and if it's a function, invoke it.

I see what you're trying to do, but it won't work. Why? makeFloat expects the value to be non-function type. It probably uses that value directly. To actually execute the function, makeFloat needs to do x() or even x.call(...) or x.apply(...), which it most certainly isn't doing.
To answer your other question i.e., can you pass functions as variables, the answer is yes. In fact, this is the way callbacks and closures are handled in Javascript. For example, in jQuery when you bind an event handler you are passing in a function as a parameter:
jQuery("#myInputId").click(function() {
...
...
});
Another way that parameters are passed in are as object attributes, for example in jQuery.ajax:
jQuery.ajax({
...
success: function(data) {
},
...
});
In both cases, click and ajax both understand and expect the parameter to be a function and not just a regular variable. For example, assuming you had an object that maintained a list of integers and you had a method called addElement(int), which expected an int parameter, you wouldn't pass in a String. It works the same way in Javascript, except for the fact that the language is not strongly typed. This is why you don't really get a type-mismatch error unless the function explicitly checks the type and throws an exception. This is generally a good practice in such language; I try to do this in the Javascript code that I write.

I've done this with string variables. You'll need to exploit the toString function.
function RefString(fn) { this.toString = function() { return String(fn()); }; }
You can use it like so:
$("#someDiv").somePlugin({optionValue: new RefString(MyFunc), ... });
function MyFunc() {
return new Date().getYear().toString();
}
It works by setting optionValue to a new OBJECT, not necessarily a function. Then anything that reads this object will ask for a value, which by default is the result of the toString function. We simply override the default behavior by executing a function that is specified when the object is constructed.
I'm not sure how it will work for EVERY plugin, but it works when a string or number is expected.

How do you mean "doesn't work"?
It looks like it should compile and run. But what happens is it executes the function and sets the value no different than if you used a constant, or called a function that wasn't inline.
What you need to do is put this line of code in an event that fires when the window is re-sized.

It looks like makeFloat is from a jQuery plugin - are you sure that the plugin is aware that 'x' can be a function and will execute it properly? From the jQuery site, it looks like it only is able to comprehend a number value or 'current' as a string, not a function.

You can pass functions as variables, yes - but that's not actually what you're asking.
What it looks like your asking is "can I set a DOM property to the result of an expression?" to which the answer is "no". (Note - not outside of browser-specific behavior such as IE's CSS Expressions - which have been deprecated in IE8 anyway)
You'll need to bind an event handler to window.onresize and use a function to update the sizing yourself.

In order for a function to be executed from a variable, it has to be called, like so:
$.option.callback.call();
Where option is the containing variable, callback is the function and call executes the function.
It's not like you don't have options though. You can set it up so that the returned value of that function is executed from the line itself. Or you can set it up in the alternative manner that you described.

You need to invoke that function so that it returns the actual value you're looking for. So you're not actually passing in a function, you're invoking it and it's immediately returning a value. For example:
$('#validate').makeFloat({
x:function(){
return $("#tabs").offset().left+$("#tabs").width();
}(),
y:70,
limitY:700
});
Notice the extra () after the function call. This invokes the function immediately, thus returning the value you're looking for.

Note that x doesn't "compute new value" when is accessed (read), but when the function is called, i.e. x(). As Chad mentioned, this is how you can automatically execute a function when windows is resized:
$(window).resize(function() {
// do something
});
[Update] After re-reading your question, I think you may be thinking overcomplicated – isn't this what you are looking for?
$('#validate').makeFloat({
x: $("#tabs").offset().left + $("#tabs").width(),
y: 70,
limitY: 700
});