[java] Java check to see if a variable has been initialized

Assuming you're interested in whether the variable has been explicitly assigned a value or not, the answer is "not really". There's absolutely no difference between a field (instance variable or class variable) which hasn't been explicitly assigned at all yet, and one which has been assigned its default value - 0, false, null etc.

Now if you know that once assigned, the value will never reassigned a value of null, you can use:

if (box != null) {
    box.removeFromCanvas();
}

(and that also avoids a possible NullPointerException) but you need to be aware that "a field with a value of null" isn't the same as "a field which hasn't been explicitly assigned a value". Null is a perfectly valid variable value (for non-primitive variables, of course). Indeed, you may even want to change the above code to:

if (box != null) {
    box.removeFromCanvas();
    // Forget about the box - we don't want to try to remove it again
    box = null;
}

The difference is also visible for local variables, which can't be read before they've been "definitely assigned" - but one of the values which they can be definitely assigned is null (for reference type variables):

// Won't compile
String x;
System.out.println(x);

// Will compile, prints null
String y = null;
System.out.println(y);

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