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On the confluence of lambda-calculus with conditional rewriting

Frédéric Blanqui 1 Claude Kirchner 1 Colin Riba 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Muller 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 beta-reduction to weakly normalizing beta-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 an extended notion of orthogonality that takes advantage of the conditional part of rewrite rules.
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Submitted on : Monday, September 11, 2006 - 3:14:01 PM
Last modification on : Thursday, March 5, 2020 - 4:53:41 PM
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Frédéric Blanqui, Claude Kirchner, Colin Riba. On the confluence of lambda-calculus with conditional rewriting. Foundations of Software Science and Computation Structures, Mar 2006, Vienne, Austria. ⟨10.1007/11690634_26⟩. ⟨inria-00000729v2⟩



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