Modular Church-Rosser Modulo

  • Jean-Pierre Jouannaud
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


In [12], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution, was later substantially simplified in [5,11].

In this paper we present a further simplification of the proof of Toyama’s result for confluence, which shows that the crux of the problem lies in two different properties: a cleaning lemma, whose goal is to anticipate the application of collapsing reductions; a modularity property of ordered completion, that allows to pairwise match the caps and alien substitutions of two equivalent terms.

We then show that Toyama’s modularity result scales up to rewriting modulo equations in all considered cases.


Normal Form Induction Hypothesis Function Symbol Critical Pair Ground Term 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Pierre Jouannaud
    • 1
  1. 1.École Polytechnique, LIX, UMR CNRS 7161PalaiseauFrance

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