siftingproperty

Siftingproperty is a concept used in mathematics and computer science to describe the behavior of a filtering operation that extracts elements from a collection according to a predicate, while preserving the original order of items. In formal terms, given a domain X and a predicate P: X → {true, false}, a filtering operator F_P acting on finite sequences S produces F_P(S) = [ x in S | P(x) = true ]. A structure or system that has the siftingproperty supports predictable composition of filters: applying F_P twice yields the same result as applying it once (idempotence), and refining the predicate does not increase the output (monotonicity with respect to refinement).

Some authors formalize the property in broader settings, such as multisets or infinite sequences, by adding stability or convergence assumptions when needed. The key elements are correctness (the sifted set contains exactly those elements that satisfy the predicate), idempotence, and compatibility with predicate refinement or combination.

Examples of siftingproperty arise in practice. In programming, list filtering using a predicate (for example, selecting even numbers) implements the siftingproperty. In databases, query selectors that return only rows meeting given conditions also exhibit this behavior. In streaming data contexts, online filters that intermittently remove or retain items based on evolving criteria can be analyzed through the lens of the siftingproperty.

Related concepts include filter operations in order theory, sieve methods in number theory, and predicate-based subobjects in category theory. The term evokes the sieve metaphor, where unwanted elements are progressively separated to reveal the target subset.