Optimal derivations in weak lambda-calculi and in orthogonal term rewriting systems
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Higher order unification via explicit substitutions
Information and Computation
Descendants and origins in term rewriting
Information and Computation - Special issue on RTA-98
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
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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.