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http://hdl.handle.net/11320/7623
Tytuł: | On Algebras of Algorithms and Specifications over Uninterpreted Data |
Autorzy: | Ivanov, Ievgen Korniłowicz, Artur Nikitchenko, Mykola |
Słowa kluczowe: | Glushkov algorithmic algebra uninterpreted data |
Data wydania: | 2018 |
Data dodania: | 4-mar-2019 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 26, Issue 2, Pages 141-147 |
Abstrakt: | This paper continues formalization in Mizar [2, 1] of basic notions of the composition-nominative approach to program semantics [13] which was started in [8, 11].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. 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 introduce a definition of the notion of a binominative function over a set D understood as a partial function which maps elements of D to D. The sets of binominative functions and nominative predicates [11] over given sets form the carrier of the generalized Glushkov algorithmic algebra [14]. 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.We formalize the operations of this algebra (also called compositions) which are valid over uninterpretated data and which include among others the sequential composition, the prediction composition, the branching composition, the monotone Floyd-Hoare composition, and the cycle composition. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [10, 12, 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/11320/7623 |
DOI: | 10.2478/forma-2018-0011 |
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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