On the Confluence of λ-Calculus with Conditional Rewriting

Abstract

The confluence of untyped #-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of #-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 #-reduction to weakly normalizing #-reduction. We also provide examples showing that outside these conditions, modularity of confluence is di#cult to achieve