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The Use of Explicit Plans to Guide Inductive Proofs
 9th Conference on Automated Deduction
, 1988
"... We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCFlike tactics, [Gordon et al 79], and by recording these specifications in a sorted metalogic, we are able to reason about the conjectures ..."
Abstract

Cited by 267 (38 self)
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We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCFlike tactics, [Gordon et al 79], and by recording these specifications in a sorted metalogic, we are able to reason about the conjectures to be proved and the methods available to prove them. In this way we can build proof plans of wide generality, formally account for and predict their successes and failures, apply them flexibly, recover from their failures, and learn them from example proofs. We illustrate this technique by building a proof plan based on a simple subset of the implicit proof plan embedded in the BoyerMoore theorem prover, [Boyer & Moore 79]. Keywords Proof plans, inductive proofs, theorem proving, automatic programming, formal methods, planning. Acknowledgements I am grateful for many long conversations with other members of the mathematical reasoning group, from which many of the ideas in this paper e...
Experiments with Proof Plans for Induction
 Journal of Automated Reasoning
, 1992
"... The technique of proof plans, is explained. This technique is used to guide automatic inference in order to avoid a combinatorial explosion. Empirical research is described to test this technique in the domain of theorem proving by mathematical induction. Heuristics, adapted from the work of Boye ..."
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Cited by 95 (33 self)
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The technique of proof plans, is explained. This technique is used to guide automatic inference in order to avoid a combinatorial explosion. Empirical research is described to test this technique in the domain of theorem proving by mathematical induction. Heuristics, adapted from the work of Boyer and Moore, have been implemented as Prolog programs, called tactics, and used to guide an inductive proof checker, Oyster. These tactics have been partially specified in a metalogic, and the plan formation program, clam, has been used to reason with these specifications and form plans. These plans are then executed by running their associated tactics and, hence, performing an Oyster proof. Results are presented of the use of this technique on a number of standard theorems from the literature. Searching in the planning space is shown to be considerably cheaper than searching directly in Oyster's search space. The success rate on the standard theorems is high. Keywords Theorem prov...
Planning and patching proof
 ARTIFICIAL INTELLIGENCE AND SYMBOLIC COMPUTATION
, 2004
"... We describe proof planning: a technique for both describing the hierarchical structure of proofs and then using this structure to guide proof attempts. When such a proof attempt fails, these failures can be analyzed and a patch formulated and applied. We also describe rippling: a powerful proof met ..."
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Cited by 3 (0 self)
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We describe proof planning: a technique for both describing the hierarchical structure of proofs and then using this structure to guide proof attempts. When such a proof attempt fails, these failures can be analyzed and a patch formulated and applied. We also describe rippling: a powerful proof method used in proof planning. We pose and answer a number of common questions about proof planning and rippling.