Experiments with proof plans for induction
Journal of Automated Reasoning
Higher-Order Annotated Terms for Proof Search
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Using Middle-Out Reasoning to Control the Synthesis of Tail-Recursive Programs
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
Automatic synthesis of recursive programs: the proof-planning paradigm
ASE '97 Proceedings of the 12th international conference on Automated software engineering (formerly: KBSE)
Higher Order Function Synthesis Through Proof Planning
Proceedings of the 16th IEEE international conference on Automated software engineering
Rippling: meta-level guidance for mathematical reasoning
Rippling: meta-level guidance for mathematical reasoning
Scheme-Based Systematic Exploration of Natural Numbers
SYNASC '06 Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Improvements in Formula Generalization
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Constructing Induction Rules for Deductive Synthesis Proofs
Electronic Notes in Theoretical Computer Science (ENTCS)
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Conjecture Synthesis for Inductive Theories
Journal of Automated Reasoning
Automating inductive proofs using theory exploration
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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We present a succinct account of dynamic rippling, a technique used to guide the automation of inductive proofs. This simplifies termination proofs for rippling and hence facilitates extending the technique in ways that preserve termination. We illustrate this by extending rippling with a terminating version of middle-out reasoning for lemma speculation. This supports automatic speculation of schematic lemmas which are incrementally instantiated by unification as the rippling proof progresses. Middle-out reasoning and lemma speculation have been implemented in higher-order logic and evaluated on typical libraries of formalised mathematics. This reveals that, when applied, the technique often finds the needed lemmas to complete the proof, but it is not as frequently applicable as initially expected. In comparison, we show that theory formation methods, combined with simpler proof methods, offer an effective alternative.