# Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm

Formalized Mathematics (2014)

- Volume: 22, Issue: 1, page 37-56
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topGrzegorz Bancerek. "Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm." Formalized Mathematics 22.1 (2014): 37-56. <http://eudml.org/doc/266729>.

@article{GrzegorzBancerek2014,

abstract = {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].},

author = {Grzegorz Bancerek},

journal = {Formalized Mathematics},

keywords = {abstract reduction systems; Knuth-Bendix algorithm},

language = {eng},

number = {1},

pages = {37-56},

title = {Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm},

url = {http://eudml.org/doc/266729},

volume = {22},

year = {2014},

}

TY - JOUR

AU - Grzegorz Bancerek

TI - Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm

JO - Formalized Mathematics

PY - 2014

VL - 22

IS - 1

SP - 37

EP - 56

AB - 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].

LA - eng

KW - abstract reduction systems; Knuth-Bendix algorithm

UR - http://eudml.org/doc/266729

ER -

## References

top- [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. Zbl06213858
- [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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.