In the monograph, STRONG ARTIFICIAL INTELLIGENCE. On the Approaches to Superintelligence, published by Sberbank, provides a cross-disciplinary review of general artificial intelligence. As an anthropomorphic direction of research, it considers Brain Principles Programming, BPP) the formalization of universal mechanisms (principles) of the brain's work with information, which are implemented at all levels of the organization of nervous tissue. This monograph provides a formalization of these principles in terms of the category theory. However, this formalization is not enough to develop algorithms for working with information. In this paper, for the description and modeling of Brain Principles Programming, it is proposed to apply mathematical models and algorithms developed by us earlier that model cognitive functions, which are based on well-known physiological, psychological and other natural science theories. The paper uses mathematical models and algorithms of the following theories: P.K.Anokhin's Theory of Functional Brain Systems, Eleonor Rosh's prototypical categorization theory, Bob Rehter's theory of causal models and natural classification. As a result, the formalization of the BPP is obtained and computer examples are given that demonstrate the algorithm's operation.