on Rewriting techniques and applications
Solving divergence in Knuth-Bendix completion by enriching signatures
Theoretical Computer Science
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
SPIKE, an Automatic Theorem Prover
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
The Use of Planning Critics in Mechanizing Inductive Proofs
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Inductive Inference for Solving Divergence in Knuth-Bendix Completion
AII '89 Proceedings of the International Workshop on Analogical and Inductive Inference
Proceedings of the 10th International Conference on Automated Deduction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
The Use of Proof Plans to Sum Series
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Termination Orderings for Rippling
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Mechanizing structural induction (formal system)
Mechanizing structural induction (formal system)
Annals of Mathematics and Artificial Intelligence
A Comparison of Two Proof Critics: Power vs. Robustness
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Sound generalizations in mathematical induction
Theoretical Computer Science
Poitín: Distilling Theorems From Conjectures
Electronic Notes in Theoretical Computer Science (ENTCS)
"Term partition" for mathematical induction
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Towards systematic analysis of theorem provers search spaces: first steps
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Perfect discrimination graphs: indexing terms with integer exponents
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a "difference matching" procedure. The critic then proposes lemmas and generalizations which "ripple" these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.