FRI: Failure-resistant induction in RRL
We have described briefly a proof manager called FRI, which supports the cover set induction method of RRL. We believe that FRI makes the cover set method more powerful and applicable to a wider class of equational theories for automating inductive proofs. Without FRI, we could not obtain a proof of the Chinese Remainder theorem .
Any successful inductive prover must be based on heuristics, which involve at least the following operations: (a) choice of induction schemes, (b) use of induction hypotheses, (c) conjecturing lemmas, (d) generalization of induction formulas, (e) simplification strategies. In addition to the heuristics provided by RRL, FRI provides the facilities to perform any of the operations listed above.
FRI can also help us to develop new heuristics for further automating cover set induction. In fact, when we started to work on Ramsey's theorem , RRL could not prove each lemma of Ramsey's theorem automatically; they were proved semi-automatically with the assistance of FRI. The semi-automatically generated proof inspired us to add new techniques to increase the automatic power of RRL. Finally, we were able to obtain an automatic proof of Ramsey's theorem.
In the near future, we will further improve FRI and plan to integrate FRI with the TECTON system developed by Kapur et al. so that proof trees created by FRI can be displayed graphically in a hypertext environment.
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