The preprint is devoted to the analysis and comparison of a number of analogies illustrating the concepts and features of functional programming languages and systems. The ideas and mechanisms of functional programming are based on the intuitive concept of functions as a fairly general approach to the representation and analysis of complex problems solutions. They are presented in the form of a correspondence between arguments and function results. The mechanism of functions has been thoroughly studied by mathematicians, which allows programmers to inherit the verified constructions of an exceptionally high modeling and demonstrative power. John McCarthy and his students were the first to demonstrate vividly the systematic application of functional programming in the methods of Lisp implementation and programming. The most obvious of these methods have been successfully assimilated into other modern programming languages and systems. As a rule, functional programming is referred to when technologies change, the role of analytics and research tasks increases, and new IT applications are discovered. The connection of functional programming with mathematical foundations allows inheriting, within the program text, the argumentation of the result construction (if achieved) involving different methods of abstracting the concepts of the problem being solved.
