Two construction functors: simple term with a variable and compound term with an operation and argument terms and schemes of term induction are introduced. The degree of construction as a number of used operation symbols is defined. Next, the term context is investigated. An x-context is a term which includes a variable x once only. The compound term is x-context iff the argument terms include an x-context once only. The context induction is shown and used many times. As a key concept, the context substitution is introduced. Finally, the translations and endomorphisms are expressed by context substitution.
@article{bwmeta1.element.doi-10_2478_forma-2014-0015,
author = {Grzegorz Bancerek},
title = {Term Context},
journal = {Formalized Mathematics},
volume = {22},
year = {2014},
pages = {125-155},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0015}
}
Grzegorz Bancerek. Term Context. Formalized Mathematics, Tome 22 (2014) pp. 125-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0015/
[1] Grzegorz Bancerek. Towards the construction of a model of Mizar concepts. Formalized Mathematics, 16(2):207–230, 2008. doi:10.2478/v10037-008-0027-x.[Crossref]
[2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.
[3] Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543–547, 1990.
[4] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589–593, 1990.
[5] Grzegorz Bancerek. On powers of cardinals. Formalized Mathematics, 3(1):89–93, 1992.
[6] Grzegorz Bancerek. Algebra of morphisms. Formalized Mathematics, 6(2):303–310, 1997.
[7] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563–567, 1990.
[8] Grzegorz Bancerek. Cartesian product of functions. Formalized Mathematics, 2(4):547– 552, 1991.
[9] Grzegorz Bancerek. Institution of many sorted algebras. Part I: Signature reduct of an algebra. Formalized Mathematics, 6(2):279–287, 1997.
[10] Grzegorz Bancerek. Free term algebras. Formalized Mathematics, 20(3):239–256, 2012. doi:10.2478/v10037-012-0029-6.[Crossref] | Zbl 1296.68085
[11] Grzegorz Bancerek. Terms over many sorted universal algebra. Formalized Mathematics, 5(2):191–198, 1996.
[12] Grzegorz Bancerek. Translations, endomorphisms, and stable equational theories. Formalized Mathematics, 5(4):553–564, 1996.
[13] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990. | Zbl 06213858
[14] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.
[15] Grzegorz Bancerek. Veblen hierarchy. Formalized Mathematics, 19(2):83–92, 2011. doi:10.2478/v10037-011-0014-5.[Crossref] | Zbl 1276.03044
[16] Grzegorz Bancerek. Reduction relations. Formalized Mathematics, 5(4):469–478, 1996.
[17] Grzegorz Bancerek. Introduction to trees. Formalized Mathematics, 1(2):421–427, 1990.
[18] Grzegorz Bancerek. König’s lemma. Formalized Mathematics, 2(3):397–402, 1991.
[19] Grzegorz Bancerek. Sets and functions of trees and joining operations of trees. Formalized Mathematics, 3(2):195–204, 1992.
[20] Grzegorz Bancerek. Joining of decorated trees. Formalized Mathematics, 4(1):77–82, 1993.
[21] Grzegorz Bancerek. Subtrees. Formalized Mathematics, 5(2):185–190, 1996.
[22] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107–114, 1990.
[23] Grzegorz Bancerek and Artur Korniłowicz. Yet another construction of free algebra. Formalized Mathematics, 9(4):779–785, 2001.
[24] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Formalized Mathematics, 4(1):91–101, 1993.
[25] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485–492, 1996.
[26] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529–536, 1990.
[27] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1): 55–65, 1990.
[28] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990. Term context 155
[29] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521–527, 1990.
[30] Czesław Byliński. Graphs of functions. Formalized Mathematics, 1(1):169–173, 1990.
[31] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990.
[32] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.
[33] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990.
[34] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841–845, 1990.
[35] Andrzej Kondracki. The Chinese Remainder Theorem. Formalized Mathematics, 6(4): 573–577, 1997.
[36] Małgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Formalized Mathematics, 5(1):61–65, 1996.
[37] Małgorzata Korolkiewicz. Many sorted quotient algebra. Formalized Mathematics, 5(1): 79–84, 1996.
[38] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477–481, 1990.
[39] Yatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1–5, 2006. doi:10.2478/v10037-006-0001-4.[Crossref]
[40] Hiroyuki Okazaki, Yuichi Futa, and Yasunari Shidama. Constructing binary Huffman tree. Formalized Mathematics, 21(2):133–143, 2013. doi:10.2478/forma-2013-0015.[Crossref] | Zbl 1298.68071
[41] Beata Perkowska. Free many sorted universal algebra. Formalized Mathematics, 5(1): 67–74, 1996.
[42] Karol Pąk. Abstract simplicial complexes. Formalized Mathematics, 18(1):95–106, 2010. doi:10.2478/v10037-010-0013-y.[Crossref]
[43] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115–122, 1990.
[44] Andrzej Trybulec. Function domains and Frænkel operator. Formalized Mathematics, 1 (3):495–500, 1990.
[45] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329–334, 1990.
[46] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97–105, 1990.
[47] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341–347, 2003.
[48] Andrzej Trybulec. A scheme for extensions of homomorphisms of many sorted algebras. Formalized Mathematics, 5(2):205–209, 1996.
[49] Andrzej Trybulec. Many sorted algebras. Formalized Mathematics, 5(1):37–42, 1996.
[50] Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15–22, 1993.
[51] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990.
[52] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569–573, 1990.
[53] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575–579, 1990.
[54] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.
[55] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73–83, 1990.
[56] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181–186, 1990.