A Proof of Finite Family Developments for Higher-Order Rewriting Using a Prefix Property

  • H. J. Sander Bruggink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


A prefix property is the property that, given a reduction, the ancestor of a prefix of the target is a prefix of the source. In this paper we prove a prefix property for the class of Higher-Order Rewriting Systems with patterns (HRSs), by reducing it to a similar prefix property of a λ-calculus with explicit substitutions. This prefix property is then used to prove that Higher-order Rewriting Systems enjoy Finite Family Developments. This property states, that reductions in which the creation depth of the redexes is bounded are finite, and is a useful tool to prove various properties of HRSs.


Local Pattern Free Variable Function Symbol Reduction Rule Object Variable 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • H. J. Sander Bruggink
    • 1
  1. 1.Department of PhilosophyUtrecht University 

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