Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm
Grzegorz Bancerek
Formalized Mathematics, Tome 22 (2014), p. 37-56 / Harvested from The Polish Digital Mathematics Library
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Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, Church- Rosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:266729 
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     author = {Grzegorz Bancerek},
     title = {Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm},
     journal = {Formalized Mathematics},
     volume = {22},
     year = {2014},
     pages = {37-56},
     zbl = {1298.68120},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0005}
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Grzegorz Bancerek. Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm. Formalized Mathematics, Tome 22 (2014) pp. 37-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0005/

[1] S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, editors. Handbook of Logic in Computer Science, chapter Term Rewriting Systems, pages 1-116. Oxford University Press, New York, 1992.

[2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[5] Grzegorz Bancerek. Minimal signature for partial algebra. Formalized Mathematics, 5 (3):405-414, 1996.

[6] Grzegorz Bancerek. Reduction relations. Formalized Mathematics, 5(4):469-478, 1996.

[7] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[8] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.

[9] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

[10] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.

[11] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[12] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[13] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[14] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[15] Jarosław Kotowicz, Beata Madras, and Małgorzata Korolkiewicz. Basic notation of universal algebra. Formalized Mathematics, 3(2):251-253, 1992.

[16] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.

[17] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.

[18] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.

[19] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.

[20] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.

[21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[22] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.

[23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

[24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.