Primitive programing algebra: general approach to a problem of functional completeness
Abstract
The goal of the research is development of scientific foundations of programming problems solutions genesis. Investigations carried out are based on algebraic research methods of programs and compositional programming methods. Basis of the last ones consists of program algebras with special classes of functions as carriers, and compositions that represent abstractions from program synthesis tools as operations. Problems of completeness in classes of computable functions that took one of the most important places in programming problems are well defined and solved in the context of program algebras. Universal method for the problem of completeness solution in primitive program algebras (PPA) on different classes of computable functions proposed in the article. Results achieved are presented as series of original statements, lemmas and theorems. The results can be applied in algebraic characteristics research of different computable functions classes in problems of programming language semantics formalization.References
Dijkstra E. A Discipline of Programming. — Prentice Hall, Inc., 1978. — 275 p.
Brooks F.P. The Design of Design: Essays from a Computer Scientist. — Addison-Wesley, 2010. — 448 p.
Brooks F.P. The Mythical Man-Month: Essays on Software Engineering. — Addison-Wesley, 1995. — 304 с.
Redko V.N. Fundamentals of compositional programming // Cybernetics and System Analysis. — 1979. — № 3. — P. 3–13.
Redko V.N. Semantical structures of software // Cybernetics and System Analysis. — 1981. — № 1. — P. 3–19.
Redko V.N. Universal program logics and their application // Proc. of 4th soviet-wide symp. — Kishenev, 1983. — P. 310–326.
Basarab I.A., Nikitchenko N.S., Redko V.N. Compositional databases. — K.: Lybid, 1992. — 92 p.
Redko I.V., Redko V.N. Existential basis of compositional paradigm // Programming and Computer Softtware. — 2008. — № 2. — P. 3–12.
Bui D.B., Redko V.N. Primitive program algebras І, ІІ // Cybernetics. – 1985. — № 1. — P. 28–33.
Bui D.B., Redko I.V. Primitive program algebras of computable functions // Cybernetics. — 1987. — № 3. — P. 68–74.
Bui D.B., Redko I.V. Primitive program algebras of functions, which preserve denotates // Report of Ukrainian AS. — 1988. — № 9. — P. 66–68.
Yershov U.L. Theory of numerations. — M.: Nauka, 1977. — 416 p.
Redko I.V., Snigur N.M. Primitive program algebra of computable functions on graph // Naukovi Visti NTUU "KPI". — 2011. — № 4. — P. 75–80.
Bogatyryova Y.O. Computability on finite sets and multi-sets // Taras Shevchenko Kiev Nation University bulletin. Ser.: phys.-math. Scienses. — 2010. — № 4. — P. 88–96.
Bogatyryova Y.O. Concept of multi-set. Structure of multi-sets family // Academitian M. Kravtchuk 13th international scientific conference, proceedings of (Kyiv, may 13–15, 2010). — K.: NTUU "KPI", 2009. — 60 p.
Maltsev A.I. Algorythmic systems. — M.: Nauka. — 1970. — 392 p.
Maltsev A.I. Constructive algebras. 1 // Uspekhi matematicheskih nauk. — 1961. — 6. — № 3. — P. 3–60.
Maltsev A.I. Algorithms and recursive functions // Groningen: Wolters-Noordhoff, 1970. — 391 p.
Cutland N. Computability. An introduction in recursive function. — M.: Mir, 1983. — 256 p.
Yershov A.P. Computability in arbitrary fields and bases // Semiotics and Informatics. — 1982. — № 19. — P. 3–58.
Maltsev A.I. Selected works // Mathematical logic and general theory of algebraic systems. — 1976. — 2. — M.: Nauka, 1976. — 388 p.