Mathematical systems theory

, Volume 13, Issue 1, pp 131–180

Infinite trees in normal form and recursive equations having a unique solution

  • Bruno Courcelle

DOI: 10.1007/BF01744293

Cite this article as:
Courcelle, B. Math. Systems Theory (1979) 13: 131. doi:10.1007/BF01744293


A system of recursive equations isC-univocal if it has a unique solution modulo the equivalence associated with a classC of interpretations. This concept yields simplified proofs of equivalence of recursive program schemes and correctness criteria for the validity of certain program transformations, provided one has syntactic easily testable conditions forC-univocality.

Such conditions are given for equational classes of interpretations. They rest upon another concept: thenormal form of an infinite tree with respect to a tree rewriting system. This concept yields a simplified construction of the Herbrand interpretation of certain equational classes of interpretations.

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.Mathématiques-InformatiqueUniversité de Bordeaux-ITalenceFrance

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