The word seems to get used in a number of contexts. The best I can figure is that they mean a variable that can't change. Isn't that what constants/finals (darn you Java!) are for?
An invariant is more "conceptual" than a variable. In general, it's a property of the program state that is always true. A function or method that ensures that the invariant holds is said to maintain the invariant.
For instance, a binary search tree might have the invariant that for every node, the key of the node's left child is less than the node's own key. A correctly written insertion function for this tree will maintain that invariant.
As you can tell, that's not the sort of thing you can store in a variable: it's more a statement about the program. By figuring out what sort of invariants your program should maintain, then reviewing your code to make sure that it actually maintains those invariants, you can avoid logical errors in your code.
It is a condition you know to always be true at a particular place in your logic and can check for when debugging to work out what has gone wrong.
I usually view them more in terms of algorithms or structures.
For example, you could have a loop invariant that could be asserted--always true at the beginning or end of each iteration. That is, if your loop was supposed to process a collection of objects from one stack to another, you could say that |stack1|+|stack2|=c, at the top or bottom of the loop.
If the invariant check failed, it would indicate something went wrong. In this example, it could mean that you forgot to push the processed element onto the final stack, etc.
The magic of wikipedia: Invariant (computer science)
In computer science, a predicate that, if true, will remain true throughout a specific sequence of operations, is called (an) invariant to that sequence.
As this line states:
In computer science, a predicate that, if true, will remain true throughout a specific sequence of operations, is called (an) invariant to that sequence.
To better understand this hope this example in C++ helps.
Consider a scenario where you have to get some values and get the total count of them in a variable called as count and add them in a variable called as sum
The invariant (again it's more like a concept):
// invariant:
// we have read count grades so far, and
// sum is the sum of the first count grades
The code for the above would be something like this,
int count=0;
double sum=0,x=0;
while (cin >> x) {
++count;
sum+=x;
}
What the above code does?
1) Reads the input from cin and puts them in x
2) After one successful read, increment count and sum = sum + x
3) Repeat 1-2 until read stops ( i.e ctrl+D)
Loop invariant:
The invariant must be True ALWAYS. So initially you start out your code with just this
while(cin>>x){
}
This loop reads data from standard input and stores in x. Well and good. But the invariant becomes false because the first part of our invariant wasn't followed (or kept true).
// we have read count grades so far, and
How to keep the invariant true?
Simple! increment count.
So ++count; would do good!. Now our code becomes something like this,
while(cin>>x){
++count;
}
But
Even now our invariant (a concept which must be TRUE) is False because now we didn't satisfy the second part of our invariant.
// sum is the sum of the first count grades
So what to do now?
Add x to sum and store it in sum ( sum+=x) and the next time
cin>>x will read a new value into x.
Now our code becomes something like this,
while(cin>>x){
++count;
sum+=x;
}
Let's check
Whether code matches our invariant
// invariant:
// we have read count grades so far, and
// sum is the sum of the first count grades
code:
while(cin>>x){
++count;
sum+=x;
}
Ah!. Now the loop invariant is True always and code works fine.
The above example was taken and modified from the book Accelerated C++ by Andrew-koening and Barbara-E
Something that doesn't change within a block of code
Following on from what it is, invariants are quite useful in writing clean code, since knowing conceptually what invariants should be present in your code allows you to easily decide how to organize your code to reach those aims. As mentioned ealier, they're also useful in debugging, as checking to see if the invariant's being maintained is often a good way of seeing if whatever manipulation you're attempting to perform is actually doing what you want it to.
It's typically a quantity that does not change under certain mathematical operations. An example is a scalar, which does not change under rotations. In magnetic resonance imaging, for example, it is useful to characterize a tissue property by a rotational invariant, because then its estimation ideally does not depend on the orientation of the body in the scanner.
The ADT invariant specifes relationships among the data fields (instance variables) that must always be true before and after the execution of any instance method.
There is an excellent example of an invariant and why it matters in the book Java Concurrency in Practice.
Although Java-centric, the example describes some code that is responsible for calculating the factors of a provided integer. The example code attempts to cache the last number provided, and the factors that were calculated to improve performance. In this scenario there is an invariant that was not accounted for in the example code which has left the code susceptible to race conditions in a concurrent scenario.
来源：https://stackoverflow.com/questions/112064/what-is-an-invariant