A proof of finite family developments for higher-order rewriting using a prefix property

Abstract

A prefix property is the property that, given a reduction, the ancestor of a prefix of the target is a prefix of the source. In this paper we prove a prefix property for the class of Higher-Order Rewriting Systems with patterns (HRSs), by reducing it to a similar prefix property of a λ-calculus with explicit substitutions. This prefix property is then used to prove that Higher-order Rewriting Systems enjoy Finite Family Developments. This property states, that reductions in which the creation depth of the redexes is bounded are finite, and is a useful tool to prove various properties of HRSs.