Graph-reducible term rewriting systems

  • Detlef Plump
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)


Term rewriting is commonly implemented by graph reduction in order to improve efficiency. In general, however, graph reduction is not complete: a term may be not normalizable through graph derivations although a normal form exists. Term rewriting systems which permit a complete implementation by graph reduction are called graph-reducible. We show that the following property is sufficient for graph-reducibility: every term having a normal form can be normalized by parallel term rewrite steps in which a rule is applied to all occurrences of some subterm. As a consequence, a broad class of term rewriting systems which includes all terminating and all orthogonal systems can be shown to be graph-reducible.


term rewriting graph reduction completeness of graph reduction 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Detlef Plump
    • 1
  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremen 33Germany

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