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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 (WMiI)
Formalized Mathematics, 2018, Volume 26, Issue 2

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