Proofs and types
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
A Lambda-to-CL Translation for Strong Normalization
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Recursive path orderings can also be incremental
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Languages: From Formal to Natural
Jumping and escaping: Modular termination and the abstract path ordering
Theoretical Computer Science
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We present a general theorem capturing conditions required for the termination of abstract reduction systems. We show that our theorem generalises another similar general theorem about termination of such systems. We apply our theorem to give interesting proofs of termination for typed combinatory logic. Thus, our method can handle most path-orderings in the literature as well as the reducibility method typically used for typed combinators. Finally we show how our theorem can be used to prove termination for incrementally defined rewrite systems, including an incremental general path ordering. All proofs have been formally machine-checked in Isabelle/HOL.