Acta Informatica

, Volume 11, Issue 2, pp 149–168 | Cite as

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

  • Wolfgang Merzenich


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.


Information System Operating System Data Structure Communication Network Information Theory 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Wolfgang Merzenich
    • 1
  1. 1.Abteilung Informatik der Universität DortmundDortmundGermany (Fed. Rep.)

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