"Opposite" of idempotent operation?

Question

What is the adjective given to a mathematical operation/expression on a variable whose new value can only be described in terms of that variable's existing value? Sequential operation?

• Example: i = i + 1
• Counter-example: i = 3 + 1

I don't know if what I call a "sequential operation" is semantically opposite to "idempotent" operation/expression but it does seem like it (e.g. the counter-example shown doesn't change value depending on how often you execute it).

Why I'm asking I'm trying to distinguish between functions in my computer program where you need to read the existing value into memory before you can compute the value from those that can be expressed as simple literals. I need to state in my design document that my program must support both cases, and I want to use the mathematically correct term for it. (note it doesn't need to be numerical, it could be string concatenation vs string overwriting).

Answer 1

"Idempotent" means that repeating the operation doesn't change the outcome. That doesn't mean that it doesn't do changes. I.e., asignment is idempotent (asign 10 five times in a row, the result will always be 10); increment isn't (doing i++ once or twice in C gives different results). Perhaps you mean it has no side effects, or is a "pure" function (each time you call it with the same arguments, the value returned is the same)? Note that e.g. $\sin x$ is pure in this sense (each time you ask for $\sin 1$ you'll get the same result), functions like printf(3) or malloc(3) in C aren't.

Answer 2

I feel that you have an invalid idea of what idempotent really means. It doesn't matter whether the outcome of the operation relates to the current value of a variable. Let me give you some examples:

• $i = 3 + 1$ is surely idempotent, while:

• $i = i + 1$ is surely not. However:

• $i = i + 0$ is idempotent, even though the new value is calculated based on the current value. Same goes for:

• $i = i * 1$, which is also idempotent. However:

• $i = rand(0, 1)$ is non-idempotent, even though it doesn't relate to it's old value.

To sum up, we say that the operation is idempotent when performing it multiple times yields the exact same result as performing it exactly once.

Answering the question asked in the subject of this thread, there are two contrasting terms:

• An operation is nullpotent, when performing it any number of times has the same result as performing it zero times.
• An operation is non-idempotent, when performing it multiple times doesn't necessarily yield the same result every time it is performed.

Let me provide another example, expanding upon example RJ Cuthbertson provided. RJ's example shows how HTTP methods work from the perspective of the client of a service. However, let's glimpse into the service's inner model:

• GET method is nullpotent. Operation of getting a resource is pure query and has no impact on the internal model.
• PUT method is idempotent. Operation of putting a resource allows the user to designate the exact location it should be made available at. Putting the same resource in the same location multiple times yields the same internal state of the system as posting it exactly once.
• POST method is non-idempotent. When posting a resource, the server decides the location it should be made available at. Posting the same resource multiple times will make it available at multiple locations.

Mind you, this is just a pure abstraction. The coder might just as well implement any of these methods to do anything he chooses. This is the way we expect it to behave, though.