Why is ++[[]][+[]]+[+[]] = “10”?

Source: http://stackoverflow.com/questions/7202157/why-is-10

If we split it up, the mess is equal to:

++[[]][+[]]
+
[+[]]

In JavaScript, it is true that +[] === 0. + converts something into a number, and in this case it will come down to +"" or 0 (see specification details below).

Therefore, we can simplify it (++ has precendence over +):

++[[]][0]
+
[0]

Because [[]][0] means: get the first element from [[]], it is true that:

[[]][0] returns the inner array ([]). Due to references it"s wrong to say [[]][0] === [], but let"s call the inner array A to avoid wrong notation.

++[[]][0] == A + 1, since ++ means "increment by one".

++[[]][0] === +(A + 1); in other words, it will always be a number (+1 does not necessarily return a number, whereas ++ always does - thanks to Tim Down for pointing this out).

Again, we can simplify the mess into something more legible. Let"s substitute [] back for A:

+([] + 1)
+
[0]

In JavaScript, this is true as well: [] + 1 === "1", because [] == "" (joining an empty array), so:

+([] + 1) === +("" + 1), and

+("" + 1) === +("1"), and

+("1") === 1

Let"s simplify it even more:

1
+
[0]

Also, this is true in JavaScript: [0] == "0", because it"s joining an array with 1 element. Joining will concatenate the elements separated by ,. With one element, you can deduce that this logic will result in the first element itself.

So, in the end we obtain (number + string = string):

1
+
"0"

=== "10" // Yay!

Specification details for +[]:

This is quite a maze, but to do +[], first it is being converted to a string because that"s what + says:

  
11.4.6 Unary + Operator
  
  
The unary + operator converts its operand to Number type.
  
  
The production UnaryExpression : + UnaryExpression is evaluated as follows:
  
  
Let expr be the result of evaluating UnaryExpression.

  
Return ToNumber(GetValue(expr)).

  

ToNumber() says:

  
Object
  
  
Apply the following steps:
  
  
Let primValue be ToPrimitive(input argument, hint String).

  
Return ToString(primValue).

  

ToPrimitive() says:

  
Object
  
  
Return a default value for the Object. The default value of an object is retrieved by calling the [[DefaultValue]] internal method of the object, passing the optional hint PreferredType. The behaviour of the [[DefaultValue]] internal method is defined by this specification for all native ECMAScript objects in 8.12.8.

[[DefaultValue]] says:

  
8.12.8 [[DefaultValue]] (hint)
  
  
When the [[DefaultValue]] internal method of O is called with hint String, the following steps are taken:
  
  
Let toString be the result of calling the [[Get]] internal method of object O with argument "toString".

  
If IsCallable(toString) is true then,

  
a. Let str be the result of calling the [[Call]] internal method of toString, with O as the this value and an empty argument list.
  
  
b. If str is a primitive value, return str.

The .toString of an array says:

  
15.4.4.2 Array.prototype.toString ( )
  
  
When the toString method is called, the following steps are taken:
  
  
Let array be the result of calling ToObject on the this value.

  
    
Let func be the result of calling the [[Get]] internal method of array with argument "join".
  

  
If IsCallable(func) is false, then let func be the standard built-in method Object.prototype.toString (15.2.4.2).

  
Return the result of calling the [[Call]] internal method of func providing array as the this value and an empty arguments list.

  

So +[] comes down to +"", because [].join() === "".

Again, the + is defined as:

  
11.4.6 Unary + Operator
  
  
The unary + operator converts its operand to Number type.
  
  
The production UnaryExpression : + UnaryExpression is evaluated as follows:
  
  
Let expr be the result of evaluating UnaryExpression.

  
Return ToNumber(GetValue(expr)).

  

ToNumber is defined for "" as:

  
The MV of StringNumericLiteral ::: [empty] is 0.

So +"" === 0, and thus +[] === 0.