On the Confluence of λ-Calculus with Conditional Rewriting

  • Frédéric Blanqui
  • Claude Kirchner
  • Colin Riba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3921)


The confluence of untyped λ-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether beta-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty’s result is improved from the assumption of strongly normalizing β-reduction to weakly normalizing β-reduction. We also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second, we go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules.


Orthonormal System Critical Pair Complete Development Proof Assistant Lambda Calculus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Frédéric Blanqui
    • 1
  • Claude Kirchner
    • 1
  • Colin Riba
    • 2
  1. 1.INRIA & LORIAFrance
  2. 2.INPL & LORIAFrance

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