Functionals and hardware

TL;DR

This paper explores the concept of functionals as hardware mechanisms for managing connections in arrays of first-order functional units, bridging higher-order abstractions with physical implementation.

Contribution

It introduces a conceptual framework for constructing hardware mechanisms based on functionals, linking higher-order abstractions to practical hardware realization.

Findings

Functionals serve as generic mechanisms for connection management in array-based systems.

A framework for hardware construction of functional mechanisms is proposed.

Discussion on the hardware realization of functionals is provided.

Abstract

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order objects, i.e. functionals are terms, and computation is term rewriting. The idea explored in the paper is that functionals correspond to generic mechanisms for management of connections in arrays consisting of first order functional units. Functionals are higher order abstractions that are useful for the management of such large arrays. Computations on higher order objects comprise dynamic configuration of connections between first order elementary functions in the arrays. Once the functionals are considered as the generic mechanisms, they have a grounding in hardware. A conceptual framework for constructing such mechanisms is presented, and their hardware realization is discussed.