A Proof of Finite Family Developments for Higher-Order Rewriting using a Prefix Property

In: Proceedings of the 17th International Conference of Term Rewriting and Applications, RTA 2006. - (Lecture Notes in Computer Science ; 4098) / Pfenning, Frank (Hrsg.)
Berlin: Springer (2006), S. 372 - 386
ISBN: 978-3-540-36834-2
Buchaufsatz / Kapitel / Fach: Informatik
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.