A.V. Chechkin - Corresponding Member of Technological Sciences Academу of the Russian Federation, Dr.Sc. (Phys.-Math.), Professor, Military Academу and the Financial University under the Government of the Russian Federation E-mail: a.chechkin@mail.ru M.V. Pirogov - Ph. D. (Phys.-Math.), Head of Sector, NPO Lavochkin (Moscow) E-mail: pmv_mvp@mail.ru

Despite growth of opportunities of means of modern informatics and scales of their application in the purposeful systems (PS), not only achievements are characteristic of the last. Serious problems are characteristic also of such systems. These problems don\'t find still satisfactory solutions. Overexpenditure of resources, ecological problems, emergencies, accidents - all this is characteristic of PS. For modern hard- and software (which should also be considered as PS) is typical not only achievements, but also principled and not fully solved problems. This, for example, the problems of verification and reliability of work of hard- and software. Modern mathematical modeling of PS based on the use of information technologies. This modeling does not cover the whole problem area of PS, and the modification of software is difficult. There is a concept that is key to problem areas of all PS. This is the concept of information system security (ISS). The path to ISS of PS lies in intellectualization of PS. Here, the intellectualization means the ability to solve in an automated way not only staff, but also non-staff tasks. The basis of intellectualization is a formalization of the problem area of PS and application of hard- and software. The analysis of means of modern informatics speaks about relevancy of the available opportunities. Nevertheless, from the point of view of need of providing ISS for PS, it is necessary to recognize means of modern informatics unsatisfactory. Therefore, it is necessary to go further. The new mathematical support of hard- and software of PS is necessary. Such ma-thematical support has to have a unified basis. It has to allow in practice coverage of expanded problem area of PS. At the same time PS, means of their development and modification have to be considered as the automated systems. Are necessary for such systems not only mathematical, program, technical and informational support. Are necessary for the automated systems as well organizational, methodical, linguistic, legal and ergonomic support (at a mathematical support priority). In the mid-eighties the academician A.P. Yershov has published the program article remaining actual. A.P. Yershov has put forward concept of the language environment and called it the Lexicon of programming. The Lexicon has phrase, semantic structure. If the program is expressed by means of the Lexicon, then it contains the description of the semantics in the text. A.P. Yershov considered that development of the Lexicon is a fine basis for formation of the knowledge base of modern programming. Authors are based on A.P. Yershov\'s ideas about the Lexicon of programming and also on results of the analysis of problems of the extending world of PS and means of modern informatics. For the solution of important problems of mathematical modeling of PS authors offer the approach based on radical modeling and radical programming. Basis of radical modeling and radical programming are the concept of environment of radicals and a formalism of schemes of radicals (universal language of schemes of radicals RADICAL). Such approach assumes construction and the operated development, evolution of environment of radicals - radical model of problem area of PS. The radical model is the uniform language environment. This environment develops and extends. It is the modeling environment realized by means of hard- and software. In full accordance with idea of the Lexicon of programming of A.P. Yershov, it is offered to create the filled-up library of radical modeling and radical programming. Scale and complexity are characteristic of modern PS. Considerable risks are connected with use of such systems. Envi-ronment of PS is changeable. Therefore in life cycle of PS expeditious use practically of any mathematical objects can be re-quired. Thus, the question of expressive opportunities of radical modeling is actual. In this regard, the question of represen-tability of mathematical objects is considered by means of radical modeling and the RADICAL language. The notion of a con-ceptual kernel of mathematics and means of mathematical modeling of problem area of TS is entered. The task of allocation of such kernel is set. (The kernel shall be formulated from the point of view of TS perspective). Also conceptual kernel of radical modeling and the RADICAL language is considered. On the basis of the considered reasons the thesis about expressive op-portunities of the RADICAL language is formulated. There are many types (variants) of automation of technology of radical programming (TRP). All such types fall in between two "extreme" types, manual and automatic. 1. Manual type of TRP (TRP-1). Schemes of radicals of radical model exist separately, and the program code exists separately. The person works with schemes of radicals and with the program code. Extent of automation is increased. 2. Automatic type of TRP (TRP-2). Only schemes of radicals of the radical model are available to the person. On the basis of schemes of radicals program codes with which the computer works are automatically generated. Such codes are directly inaccessible to the person. In case of TRP-2 the RADICAL language is the latest programming language (in this consideration). Experience of development of hard- and software of PS allows to speak about expediency of development of TRP and radical modeling, including, within the real automated systems. The list of containers - schemes of the radicals characteristic of problem areas of the automated systems is provided in article. The short description of the typical automated system is provided. Among the directions of further researches in the field of radical modeling and radical programming development of the editor of schemes of radicals and development of the initial atlas of schemes of the radicals characteristic of the PS problem area are paramount. Also developing distributed system uniting the experts dividing basic provisions of radical modeling and radical programming is necessary. Purpose of such system - the analysis of a condition of a problem area of PS and means of informatics; development of offers on work planning on creation of instruments of automation of PS based on application of radical modeling; operational exchange of information.

 

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