Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Rewrite orderings for higher-order terms in n-long &bgr;-normal form and the recursive path ordering
Theoretical Computer Science - Special issue on rewriting techniques and applications
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
A Monotonic Higher-Order Semantic Path Ordering
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Strict Functionals for Termination Proofs
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Complete Monotonic Semantic Path Orderings
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Termination and Reduction Checking for Higher-Order Logic Programs
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Termination of Combined (Rewrite and lambda-Calculus) Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
A Monotonic Higher-Order Semantic Path Ordering
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
The Computability Path Ordering: The End of a Quest
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Harnessing first order termination provers using higher order dependency pairs
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Semantic labelling for proving termination of combinatory reduction systems
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
Orderings and constraints: theory and practice of proving termination
Rewriting Computation and Proof
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There is an increasing use of (first- and higher-order) rewrite rules in many programming languages and logical systems. The recursive path ordering (RPO) is a well-known tool for proving termination of such rewrite rules in the first-order case. However, RPO has some weaknesses. For instance, since it is a simplification ordering, it can only handle simply terminating systems. Several techniques have been developed for overcoming these weaknesses of RPO. A very recent such technique is the monotonic semantic path ordering (MSPO), a simple and easily automatable ordering which generalizes other more ad-hoc methods. Another recent extension of RPO is its higher-order version HORPO. HORPO is an ordering on terms of a typed lambda-calculus generated by a signature of higher-order function symbols. Although many interesting examples can be proved terminating using HORPO, it inherits the weaknesses of the first-order RPO. Therefore, there is an obvious need for higher-order termination orderings without these weaknesses. Here we define the first such ordering, the monotonic higher-order semantic path ordering (MHOSPO), which is still automatable like MSPO. We give evidence of its power by means of several natural and non-trivial examples which cannot be handled by HORPO.