Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

Terms Over Many Sorted Universal Algebra


Grzegorz Bancerek
Institute of Mathematics, Polish Academy of Sciences

Summary.

Pure terms (without constants) over a signature of many sorted universal algebra and terms with constants from algebra are introduced. Facts on evaluation of a term in some valuation are proved.

This article has been prepared during the visit of the author in Nagano in Summer 1994.

MML Identifier: MSATERM

The terminology and notation used in this paper have been introduced in the following articles [18] [12] [23] [21] [24] [10] [8] [11] [14] [1] [4] [16] [2] [22] [3] [13] [5] [6] [7] [19] [20] [9] [15] [17]

Contents (PDF format)

  1. Terms over a Signature and over an Algebra
  2. Sort of a Term
  3. Argument Sequence
  4. Compound Terms
  5. Evaluation of Terms

Bibliography

[1] Grzegorz Bancerek. Introduction to trees. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[3] Grzegorz Bancerek. Cartesian product of functions. Journal of Formalized Mathematics, 3, 1991.
[4] Grzegorz Bancerek. K\"onig's Lemma. Journal of Formalized Mathematics, 3, 1991.
[5] Grzegorz Bancerek. Sets and functions of trees and joining operations of trees. Journal of Formalized Mathematics, 4, 1992.
[6] Grzegorz Bancerek. Joining of decorated trees. Journal of Formalized Mathematics, 5, 1993.
[7] Grzegorz Bancerek. Subtrees. Journal of Formalized Mathematics, 6, 1994.
[8] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[9] Grzegorz Bancerek and Piotr Rudnicki. On defining functions on trees. Journal of Formalized Mathematics, 5, 1993.
[10] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[11] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[12] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[13] Patricia L. Carlson and Grzegorz Bancerek. Context-free grammar --- part I. Journal of Formalized Mathematics, 4, 1992.
[14] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[15] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[16] Andrzej Nedzusiak. $\sigma$-fields and probability. Journal of Formalized Mathematics, 1, 1989.
[17] Beata Perkowska. Free many sorted universal algebra. Journal of Formalized Mathematics, 6, 1994.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[20] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[21] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[22] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[23] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received November 25, 1994

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