Abstract
In the absence of termination, confluence of rewriting systems is often hard to establish. The class of orthogonal rewriting systems is the main class of not-necessarily-terminating, but confluent rewriting systems. The reason why confluence holds in orthogonal rewriting systems is the absence of the so-called critical pairs, making that rewrite steps never interfere (in a destructive way) with one another. We discuss some ways to adapt the confluence by orthogonality proof method to rewriting systems having ‘innocent’ critical pairs. Confluence results are obtained for lambda calculus with beta, eta and omega rules, lambda calculi with restricted expansion rules and for (first- and higher-order) term rewriting systems for which all critical pairs are development closed.
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