A Proof of Finite Family Developments for Higher-Order Rewriting using a Prefix Property
A prefix property is the property that, given a reduction, the ancestor of a prefix of the target is a prefix of the source of the reduction. In this paper we prove a prefix property for the class of Higher-order Rewrite Systems with pattern (HRSs), by reducing it to a similar property of a $\lambda$-calculus with explicit substitutions. This prefix property is then used to prove that Higher-order Rewrite 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.
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