Handbook of logic in artificial intelligence and logic programming
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Lemma Discovery in Automated Induction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Mechanizing structural induction (formal system)
Mechanizing structural induction (formal system)
Journal of Automated Reasoning
Rippling: meta-level guidance for mathematical reasoning
Rippling: meta-level guidance for mathematical reasoning
Reasoning about incompletely defined programs
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automation for Dependently Typed Functional Programming
Fundamenta Informaticae - Dependently Typed Programming
Dynamic rippling, middle-out reasoning and lemma discovery
Verification, induction termination analysis
Dynamic rippling, middle-out reasoning and lemma discovery
Verification, induction termination analysis
Case-Analysis for rippling and inductive proof
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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For proofs by induction it is often necessary to generalize statements to strengthen the induction hypotheses. This paper presents improved heuristics to generalize away subterms, unnecessary conditions and function symbols in a formula. This resolves shortcomings that we encountered within an experimental evaluation of generalization heuristics from the literature. Our generalization method has been implemented in the verification tool $\checkmark$ eriFun. An evaluation with examples from the literature as well as several case studies of our own demonstrates the success of our development.