A computational logic handbook
A computational logic handbook
Satisfiability of systems of ordinal notations with the subterm property is decidable
Proceedings of the 18th international colloquium on Automata, languages and programming
A logic programming approach to implementing higher-order term rewriting
ELP'91 Conference Proceedings on Extensions of logic programming
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
IMPS: an interactive mathematical proof system
Journal of Automated Reasoning
Term rewriting and all that
Higher-Order Annotated Terms for Proof Search
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
An Ordinal Calculus for Proving Termination in Term Rewriting
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
The Use of Embeddings to Provide a Clean Separation of Term and Annotation for Higher Order Rippling
Journal of Automated Reasoning
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This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in λClam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.