Defining Idempotence

Question

So "idempotence" can be defined as:

An action, that if performed N times has the same effect as performing the action only once.

Got it, easy enough.

My question is about the subtlety of this definition -is an action considered idempotent by itself, or must you also consider the data being passed into the action?

Let me clarify with an example:

Suppose I have a PUT method that updates some resource, we'll call it f(x)

Obviously, f(3) is idempotent, as long as I supply 3 as the input. And equally obvious, f(5) will change the value of the resource (i.e., it will no longer be 3 or whatever value was there previously)

So when we talk about idempotence, are we referring to the generalization of the action/function like (i.e., f(x)), or are we referring to action/function + the data being passed into it (i.e., f(3))?

Answer 1

Suppose I have a PUT method that updates some resource, we'll call it f(x)

Obviously, f(3) is idempotent, as long as I supply 3 as the input. And equally obvious, f(5) will change the value of the resource (i.e., it will no longer be 3 or whatever value was there previously).

This is only obvious is the server implementation is such that PUT respects this idempotent property. In the context of HTTP, RFC 2616 says:

Methods can also have the property of "idempotence" in that (aside from error or expiration issues) the side-effects of N > 0 identical requests is the same as for a single request.

Going a bit off topic... In a distributed system like the web, you may also want to consider commutativity and concurrent requests. For example N+1 of the same PUT(x1) request should have the same effect, but you don't know if another client made a different PUT(x2) request in between yours, so while nPUT(x1)=PUT(x1) and mPUT(x2)=PUT(x2), the two sets of requests could be interleaved.

Answer 2

Idempotence requires that the action holds for all values over its domain, i.e., f(f(x)) = f(x) for all x. Another way to think about it is that an operation is idempotent if the composition of the operation with itself is just that operation.