Lambda-calculus, combinators and applicative computational technologies

Abstract

Applicative computing systems and technologies have taken a strong position in modern computing. In this paper, the basic applicative system, whether it is a lambda calculus or a system of combinators, is considered as a prototype concept system, using which it is possible to build individual systems that are practically significant for mathematics, computing, or programming. They are families of computational models that have both their own semantics and applied areas. This conceptualization/individualization technique is characteristic of the field of semantic studies. As it turns out, the applicative approach forms a metatheoretical framework that provides the basis for cognitive systems that consider abstract objects and interpret their properties and behavior in the environment of modern computing.