Skip to main content
SpringerLink
Log in

A binary operation on trees and an initial algebra characterization for finite tree types

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

A binary operation on the class of trees is defined that generates a set B of finite trees form a trivial tree (one node) and B contains for every finite tree G exactly one element isomorphic to G. The binary operation defines an algebraic structure on B, and as a consequence the finite tree types are characterized as an initial algebra in the same way as the natural numbers are characterized as an initial algebra by the Peano-Lawvere axiom [2]. Simple and primitive recursion are defined and some applications of the initial algebra characterization are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arbib, M.A., Manes, E.G.: Arrows, structures and functors. New York: Academic Press 1975

    Google Scholar 

  2. Birkhoff, G., MacLane, S.: Algebra. New York: Macmillan 1968

    Google Scholar 

  3. Comtet, L.: Advanced combinatorics. Boston: Dordrecht 1974

    Google Scholar 

  4. Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial algebra approach to the specification, correctness and implementation of abstract data types. IBM Research Report RC 6487, 1977

  5. Eilenberg, S., Wright, J.B.: Automata in general algebras. Information and Control 11, 452–470 (1967)

    Google Scholar 

  6. Give'on, Y., Arbib, M.A.: Algebra automata. II. The categorical framework for dynamic analysis. Information and Control 12, 346–370 (1968)

    Google Scholar 

  7. Grätzer, G.: Universal algebra. Princeton: Van Nostrand 1968

    Google Scholar 

  8. Harary, F., Plamer, E.M.: Graphical enumeration. New York: Academic Press 1966

    Google Scholar 

  9. MacLane, S.: Categories for the working mathematician. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  10. Mezei, J., Wright, J.B.: Generalized ALGOL-like languages. IBM Research Report RC 1528, 1965

  11. Oberschelp, W., Wille, D.: Mathematischer Einführungskurs für Informatiker. Stuttgart: Teubner 1976

    Google Scholar 

  12. Pareigis, B.: Categories and functors. New York: Academic Press 1970

    Google Scholar 

  13. Schmidt, J.: Mengenlehre, Bd. I. Mannheim: B.I. 1966

    Google Scholar 

  14. Thatcher, J.W.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. J. Comput. System Sci. 1, 317–322 (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung Informatik der Universität Dortmund, D-4600, Dortmund, Germany (Fed. Rep.)

    Wolfgang Merzenich

Authors
  1. Wolfgang Merzenich
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merzenich, W. A binary operation on trees and an initial algebra characterization for finite tree types. Acta Informatica 11, 149–168 (1979). https://doi.org/10.1007/BF00264022

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00264022

Keywords

Search

Navigation