Remnantpartial

Remnantpartial is a term used in theoretical discussions of systems that undergo pruning, reduction, or truncation to denote the fragment that remains defined on a subset of the original domain. The name combines the idea of a remnant—a remaining piece of a larger whole—with a partial object, which is not defined everywhere.

Definition: Let X be a set or space equipped with a structure S (for example a function f: X → Y, a topological space, or an algebraic object). A remnantpartial is a pair (Dom, f|Dom) where Dom ⊆ X and f|Dom is the restriction of f to Dom. It represents the surviving portion of the original object after a remnant operation R that reduces X to a subdomain X' ⊆ X. The remnantpartial is nontrivial when Dom is nonempty and the restricted structure carries meaningful information.

Contexts and use: In computation, remnantpartial can describe the result of pruning a search tree or dataset, where the computation or data is only defined on the surviving indices. In mathematics or theoretical computer science, it can model restricted morphisms after an idempotent projection or truncation, capturing how much structure remains after reduction.

Relation to related concepts: It is related to subobjects and partial functions, but emphasizes origin in a pruning or remnant process. The term is used in niche or emerging discussions and may vary in exact definition across disciplines.

See also: partial function, restriction, remnant, truncation, residual.