What is an idempotent operation?

In computing, an idempotent operation is one that has no additional effect if it is called more than once with the same input parameters. For example, removing an item from a set can be considered an idempotent operation on the set.

In mathematics, an idempotent operation is one where f(f(x)) = f(x). For example, the abs() function is idempotent because abs(abs(x)) = abs(x) for all x.

These slightly different definitions can be reconciled by considering that x in the mathematical definition represents the state of an object, and f is an operation that may mutate that object. For example, consider the Python set and its discard method. The discard method removes an element from a set, and does nothing if the element does not exist. So:

my_set.discard(x)

has exactly the same effect as doing the same operation twice:

my_set.discard(x)
my_set.discard(x)

Idempotent operations are often used in the design of network protocols, where a request to perform an operation is guaranteed to happen at least once, but might also happen more than once. If the operation is idempotent, then there is no harm in performing the operation two or more times.

See the Wikipedia article on idempotence for more information.

^{The above answer previously had some incorrect and misleading examples. Comments below written before April 2014 refer to an older revision.}

An idempotent operation can be repeated an arbitrary number of times and the result will be the same as if it had been done only once. In arithmetic, adding zero to a number is idempotent.

Idempotence is talked about a lot in the context of "RESTful" web services. REST seeks to maximally leverage HTTP to give programs access to web content, and is usually set in contrast to SOAP-based web services, which just tunnel remote procedure call style services inside HTTP requests and responses.

REST organizes a web application into "resources" (like a Twitter user, or a Flickr image) and then uses the HTTP verbs of POST, PUT, GET, and DELETE to create, update, read, and delete those resources.

Idempotence plays an important role in REST. If you GET a representation of a REST resource (eg, GET a jpeg image from Flickr), and the operation fails, you can just repeat the GET again and again until the operation succeeds. To the web service, it doesn't matter how many times the image is gotten. Likewise, if you use a RESTful web service to update your Twitter account information, you can PUT the new information as many times as it takes in order to get confirmation from the web service. PUT-ing it a thousand times is the same as PUT-ing it once. Similarly DELETE-ing a REST resource a thousand times is the same as deleting it once. Idempotence thus makes it a lot easier to construct a web service that's resilient to communication errors.

Further reading: RESTful Web Services, by Richardson and Ruby (idempotence is discussed on page 103-104), and Roy Fielding's PhD dissertation on REST. Fielding was one of the authors of HTTP 1.1, RFC-2616, which talks about idempotence in section 9.1.2.

No matter how many times you call the operation, the result will be the same.

Idempotence means that applying an operation once or applying it multiple times has the same effect.

Examples:

• Multiplication by zero. No matter how many times you do it, the result is still zero.
• Setting a boolean flag. No matter how many times you do it, the flag stays set.
• Deleting a row from a database with a given ID. If you try it again, the row is still gone.

For pure functions (functions with no side effects) then idempotency implies that f(x) = f(f(x)) = f(f(f(x))) = f(f(f(f(x)))) = ...... for all values of x

For functions with side effects, idempotency furthermore implies that no additional side effects will be caused after the first application. You can consider the state of the world to be an additional "hidden" parameter to the function if you like.

Note that in a world where you have concurrent actions going on, you may find that operations you thought were idempotent cease to be so (for example, another thread could unset the value of the boolean flag in the example above). Basically whenever you have concurrency and mutable state, you need to think much more carefully about idempotency.

Idempotency is often a useful property in building robust systems. For example, if there is a risk that you may receive a duplicate message from a third party, it is helpful to have the message handler act as an idempotent operation so that the message effect only happens once.

A good example of understanding an idempotent operation might be locking a car with remote key.

log(Car.state) // unlocked

Remote.lock();
log(Car.state) // locked

Remote.lock();
Remote.lock();
Remote.lock();
log(Car.state) // locked

lock is an idempotent operation. Even if there are some side effect each time you run lock, like blinking, the car is still in the same locked state, no matter how many times you run lock operation.

An idempotent operation produces the result in the same state even if you call it more than once, provided you pass in the same parameters.

It is any operation that every nth result will result in an output matching the value of the 1st result. For instance the absolute value of -1 is 1. The absolute value of the absolute value of -1 is 1. The absolute value of the absolute value of absolute value of -1 is 1. And so on.

See also: When would be a really silly time to use recursion?

An idempotent operation over a set leaves its members unchanged when applied one or more times.

It can be a unary operation like absolute(x) where x belongs to a set of positive integers. Here absolute(absolute(x)) = x.

It can be a binary operation like union of a set with itself would always return the same set.

cheers

An operation is said to be idempotent if executing it multiple times is equivalent to executing it once.

For eg: setting volume to 20. No matter how many times the volume of TV is set to 20, end result will be that volume is 20. Even if a process executes the operation 50/100 times or more, at the end of the process the volume will be 20.

Counter example: increasing the volume by 1. If a process executes this operation 50 times, at the end volume will be initial Volume + 50 and if a process executes the operation 100 times, at the end volume will be initial Volume + 100. As you can clearly see that the end result varies based upon how many times the operation was executed. Hence, we can conclude that this operation is NOT idempotent.

I have highlighted the end result in bold.

If you think in terms of programming, let's say that I have an operation in which a function f takes foo as the input and the output of f is set to foo back. If at the end of the process (that executes this operation 50/100 times or more), my foo variable holds the value that it did when the operation was executed only ONCE, then the operation is idempotent, otherwise NOT.

foo = <some random value here, let's say -2>

{ foo = f( foo ) }   curly brackets outline the operation

if f returns the square of the input then the operation is NOT idempotent. Because foo at the end will be (-2) raised to the power (number of times operation is executed)

if f returns the absolute of the input then the operation is idempotent because no matter how many multiple times the operation is executed foo will be abs(-2).
Here, end result is defined as the final value of variable foo.

In mathematical sense, idempotence has a slightly different meaning of:
f(f(....f(x))) = f(x)
here output of f(x) is passed as input to f again which doesn't need to be the case always with programming.

my 5c: In integration and networking the idempotency is very important. Several examples from real-life: Imagine, we deliver data to the target system. Data delivered by a sequence of messages. 1. What would happen if the sequence is mixed in channel? (As network packages always do :) ). If the target system is idempotent, the result will not be different. If the target system depends of the right order in the sequence, we have to implement resequencer on the target site, which would restore the right order. 2. What would happen if there are the message duplicates? If the channel of target system does not acknowledge timely, the source system (or channel itself) usually sends another copy of the message. As a result we can have duplicate message on the target system side. If the target system is idempotent, it takes care of it and result will not be different. If the target system is not idempotent, we have to implement deduplicator on the target system side of the channel.

For a workflow manager (as Apache Airflow) if an idempotency operation fails in your pipeline the system can retry the task automatically without affecting the system. Even if the logs change, that is good because you can see the incident.

The most important in this case is that your system can retry the task that failed and doesn't mess up the pipeline (e.g. appending the same data in a table each retry)

Let's say the client makes a request to "IstanceA" service which process the request, passes it to DB, and shuts down before sending the response. since the client does not see that it was processed and it will retry the same request. Load balancer will forward the request to another service instance, "InstanceB", which will make the same change on the same DB item.

We should use idempotent tokens. When a client sends a request to a service, it should have some kind of request-id that can be saved in DB to show that we have already executed the request. if the client retries the request, "InstanceB" will check the requestId. Since that particular request already has been executed, it will not make any change to the DB item. Those kinds of requests are called idempotent requests. So we send the same request multiple times, but we won't make any change