The main scientific directions and the most important results of the school
The main direction of scientific research of the school is explicit programming – the theory of descriptive and declarative program algebroids (algebraic structures that are formal and adequate models of data structures, programs and software design tools). For these structures the problems of existence, unambiguity and effective task are solved, which lays the foundation of a new direction of computer science – programmology – science of programs and logic of programming. Within this direction it was possible to give a complete solution to a set of problems that are fundamental to the ways of further development of computer science, namely:
- Kline’s problem of axiomatization of regular and quasi-regular algebras;
- Chorch-Kutland problem on the completeness of integer computable functions and similar problems of Tarsky and Maltsev for the functions of rational, lexical argument and meaning;
- completeness problem for classes of computed functions and compositions;
- problems of clarification of manipulative actions in databases and completeness of the corresponding class of functions – functions which store denotations;
- the problem of construction and research of semantically oriented compositional logics of the first order of partial functions;
- problem of complete and natural task of SQL-like languages.