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http://hdl.handle.net/11320/7624
Tytuł: | On an Algorithmic Algebra over Simple-Named Complex-Valued Nominative Data |
Autorzy: | Ivanov, Ievgen Korniłowicz, Artur Nikitchenko, Mykola |
Słowa kluczowe: | Glushkov algorithmic algebra nominative data |
Data wydania: | 2018 |
Data dodania: | 4-mar-2019 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 26, Issue 2, Pages 149-158 |
Abstrakt: | This paper continues formalization in the Mizar system [2, 1] of basic notions of the composition-nominative approach to program semantics [14] which was started in [8, 12, 10].The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. In particular, data in computer systems are modeled as nominative data [15]. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3].In the paper we give a formal definition of the notions of a binominative function over given sets of names and values (i.e. a partial function which maps simple-named complex-valued nominative data to such data) and a nominative predicate (a partial predicate on simple-named complex-valued nominative data). The sets of such binominative functions and nominative predicates form the carrier of the generalized Glushkov algorithmic algebra for simple-named complex-valued nominative data [15]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties.In particular, we formalize the operations of this algebra which require a specification of a data domain and which include the existential quantifier, the assignment composition, the composition of superposition into a predicate, the composition of superposition into a binominative function, the name checking predicate. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [11, 13, 9]. |
Afiliacja: | Ievgen Ivanov - Taras Shevchenko National University, Kyiv, Ukraine Artur Korniłowicz - Institute of Informatics, University of Białystok, Poland Mykola Nikitchenko - Taras Shevchenko National University, Kyiv, Ukraine |
URI: | http://hdl.handle.net/11320/7624 |
DOI: | 10.2478/forma-2018-0012 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
metadata.dc.identifier.orcid: | brakorcid 0000-0002-4565-9082 0000-0002-4078-1062 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2018, Volume 26, Issue 2 |
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