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  2. Czasopisma naukowe / Journals
  3. Formalized Mathematics
  4. Formalized Mathematics, 2012, Volume 20, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3657
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    dc.contributor.authorBancerek, Grzegorz-
    dc.date.accessioned2015-12-06T19:06:09Z-
    dc.date.available2015-12-06T19:06:09Z-
    dc.date.issued2012-
    dc.identifier.citationFormalized Mathematics, Volume 20, Issue 4, 2012, Pages 309-341-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3657-
    dc.description.abstractWe introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms.-
    dc.description.sponsorshipThis work has been supported by the Polish Ministry of Science and Higher Education project “Managing a Large Repository of Computer-verified Mathematical Knowledge” (N N519 385136).-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleProgram Algebra over an Algebra-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-012-0037-6-
    dc.description.AffiliationFaculty of Computer Science, Białystok Technical University, Wiejska 45A, 15-351 Białystok, Poland-
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
    dc.description.referencesGrzegorz Bancerek. Introduction to trees. Formalized Mathematics, 1(2):421-427, 1990.-
    dc.description.referencesGrzegorz Bancerek. K¨onig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.-
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
    dc.description.referencesGrzegorz Bancerek. Cartesian product of functions. Formalized Mathematics, 2(4):547-552, 1991.-
    dc.description.referencesGrzegorz Bancerek. K¨onig’s lemma. Formalized Mathematics, 2(3):397-402, 1991.-
    dc.description.referencesGrzegorz Bancerek. Algebra of morphisms. Formalized Mathematics, 6(2):303-310, 1997.-
    dc.description.referencesGrzegorz Bancerek. Institution of many sorted algebras. Part I: Signature reduct of an algebra. Formalized Mathematics, 6(2):279-287, 1997.-
    dc.description.referencesGrzegorz Bancerek. Mizar analysis of algorithms: Preliminaries. Formalized Mathematics, 15(3):87-110, 2007, doi:10.2478/v10037-007-0011-x.-
    dc.description.referencesGrzegorz Bancerek. Sorting by exchanging. Formalized Mathematics, 19(2):93-102, 2011, doi: 10.2478/v10037-011-0015-4.-
    dc.description.referencesGrzegorz Bancerek. Free term algebras. Formalized Mathematics, 20(3):239-256, 2012, doi: 10.2478/v10037-012-0029-6.-
    dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
    dc.description.referencesGrzegorz Bancerek and Piotr Rudnicki. The set of primitive recursive functions. Formalized Mathematics, 9(4):705-720, 2001.-
    dc.description.referencesGrzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.-
    dc.description.referencesEwa Burakowska. Subalgebras of the universal algebra. Lattices of subalgebras. Formalized Mathematics, 4(1):23-27, 1993.-
    dc.description.referencesCzesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.-
    dc.description.referencesCzesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.-
    dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
    dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
    dc.description.referencesCzesław Bylinski. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.-
    dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
    dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
    dc.description.referencesArtur Korniłowicz. On the group of automorphisms of universal algebra & many sorted algebra. Formalized Mathematics, 5(2):221-226, 1996.-
    dc.description.referencesArtur Korniłowicz and Marco Riccardi. The Borsuk-Ulam theorem. Formalized Mathematics, 20(2):105-112, 2012, doi: 10.2478/v10037-012-0014-0-
    dc.description.referencesMałgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Formalized Mathematics, 5(1):61-65, 1996.-
    dc.description.referencesJarosław Kotowicz, Beata Madras, and Małgorzata Korolkiewicz. Basic notation of universal algebra. Formalized Mathematics, 3(2):251-253, 1992.-
    dc.description.referencesYatsuka Nakamura and Grzegorz Bancerek. Combining of circuits. Formalized Mathematics, 5(2):283-295, 1996.-
    dc.description.referencesAndrzej Nedzusiak. Probability. Formalized Mathematics, 1(4):745-749, 1990.-
    dc.description.referencesBeata Perkowska. Free many sorted universal algebra. Formalized Mathematics, 5(1):67-74, 1996.-
    dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.-
    dc.description.referencesAndrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.-
    dc.description.referencesAndrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.-
    dc.description.referencesAndrzej Trybulec. Many sorted algebras. Formalized Mathematics, 5(1):37-42, 1996.-
    dc.description.referencesAndrzej Trybulec. A scheme for extensions of homomorphisms of many sorted algebras. Formalized Mathematics, 5(2):205-209, 1996.-
    dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.-
    dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.-
    dc.description.referencesWojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.-
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
    dc.description.referencesTetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.-
    dc.description.referencesEdmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
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