Higher-Order (Non-)Modularity

We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints.

• Type: Conference
• Year: 2010
• Where: RTA
• Authors: Claus Appel, Vincent van Oostrom, Jakob Grue Simonsen
• Keywords: RTA 2010, Suitable Linearity Constraints, Term Rewriting, Term Rewriting Systems, Theoretical Computer Science