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in imperative programming, a subroutine with side effects is idempotent if multiple calls to the subroutine have the same effect on the system state as a single call, in other words if the function from the system state space to itself associated with the subroutine is idempotent in the mathematical sense given in the definition; in functional ...
A subroutine with side effects is idempotent if multiple applications of the subroutine have the same effect on the system state as a single application, in other words if the function from the system state space to itself associated with the subroutine is idempotent in the mathematical sense. For instance, consider the following Python program:
The compare function is included to illustrate a partial order on the states. The merge function is commutative, associative, and idempotent. The update function monotonically increases the internal state according to the compare function. This is thus a correctly defined state-based CRDT and will provide strong eventual consistency.
A substitution σ is called idempotent if σσ = σ, and hence tσσ = tσ for every term t. When x i ≠t i for all i, the substitution { x 1 ↦ t 1, …, x k ↦ t k} is idempotent if and only if none of the variables x i occurs in any t j. Substitution composition is not commutative, that is, στ may be different from τσ, even if σ and ...
Idempotent matrices arise frequently in regression analysis and econometrics. For example, in ordinary least squares , the regression problem is to choose a vector β of coefficient estimates so as to minimize the sum of squared residuals (mispredictions) e i : in matrix form,
The reason reentrant is sometimes called idempotent is that in imperative programming, the effect of a piece of code is thought of as what modifications it causes to be made to the program state, and that effect can be modeled as a function on the space of potential program states - reentrance then is idempotence of that function.
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.
R is idempotent if R = S. Equivalently, relation R is idempotent if and only if the following two properties are true: R is a transitive relation, meaning that R ∘ R ⊆ R. Equivalently, in terms of individual elements, for every x, y, and z for which xRy and yRz are both true, xRz is also true. R ∘ R ⊇ R.