functionalsobjects

Functionalsobjects is a term used in certain cross-disciplinary discussions to describe objects that encode functionals in an object-oriented or type-theoretic setting. The expression is not standardized and may be used differently in mathematics, functional programming, or category theory, where it serves to bridge abstract functionals with concrete data representations.

In broad terms, a functionalsobject represents a functional—an entity that maps a function to a scalar or to another function—while also behaving as an object that can be stored, passed as a value, and composed with other objects. This hybrid view emphasizes both the evaluative role of a functional and the mutable, higher-level properties of an object.

Mathematical perspective: functionalsobjects can be seen as a structured wrapper around a functional, carrying metadata such as domain, codomain, linearity, continuity, and a method for evaluation. Computationally, they resemble function objects or functors that capture a callable plus state, enabling programming patterns such as higher-order functions, closures, and currying.

Examples include the evaluation-at-a-point functional F(f) = f(x0) and the more general integral-type functional F(f) = ∫ w(x) f(x) dx. A functionalsobject would provide an interface to apply to f, while preserving the ability to be composed with other functionals or stored in data structures.

Relation to related concepts: function objects, functors, and higher-order functions share overlapping ideas with functionalsobjects, but the latter emphasizes the functional-analytic origin within an object-centric formulation. Usage is primarily in theoretical discussions, language design, or numerical frameworks that treat functionals as first-class citizens.