Nikitchenko M. Theory of integrated composition nominative program models.

A general theory of program models, based on principles of development, compositionality and nominativity is developed. A formalism of composition nominative systems, which represent program models of various abstraction and generality levels and which permits program adequate specification and effective realisation, is proposed and investigated. Subclasses of such systems, which represent infinitary predicate logics of various types, are investigated. Classical problems of correctness and completeness are solved for such logics. Program computability methods, which generalise traditional approaches to computability, are defined and investigated. The complete classes of computable functions and compositions over nominative data of various abstraction and generality levels are defined and algebraic representations of such classes are constructed.