Idempotence

Idempotence is a property of certain operations in mathematics and computer science. An operation is idempotent if applying it once or repeatedly has the same effect as applying it a single time. Formally, for a function f, f(f(x)) = f(x) for all x in its domain. In many contexts idempotence refers to actions that do not compound or change the outcome when performed again.

In computing and distributed systems, idempotence is desirable for reliability and fault tolerance. It means that receiving the same request multiple times due to retries or network failures does not change the end state beyond the initial application. In programming, an idempotent function yields the same output and state whether called once or many times, provided the inputs remain the same.

Common examples include HTTP methods: GET and HEAD are safe and idempotent, and PUT and DELETE are designed to be idempotent so repeated calls do not alter the result after the first application. POST is typically non-idempotent, since it usually creates new resources, but it can be made idempotent with the use of unique idempotency keys. In databases and APIs, updating a resource with the same values is idempotent, and deleting a resource that is already absent remains idempotent. Setting a field to a constant value is another idempotent operation.

Design and implementation considerations: achieving idempotence often requires modeling operations as state transitions and avoiding side effects that accumulate on repeated execution. Developers may use idempotency keys, idempotent retries, and careful resource handling to ensure safe retries. Idempotence concerns the end state rather than the number of invocations and does not by itself guarantee security or correctness.

In mathematics, an element a is idempotent if a·a = a. In functional programming, a function f is idempotent if f(f(x)) = f(x) for all x.