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72
IsaPlanner: A prototype proof planner in Isabelle
 In Proceedings of CADE’03, LNCS
, 2003
"... Abstract. IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. This paper introduces our approach to proof planning, gives and overview o ..."
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Cited by 29 (10 self)
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Abstract. IsaPlanner is a generic framework for proof planning in the interactive theorem prover Isabelle. It facilitates the encoding of reasoning techniques, which can be used to conjecture and prove theorems automatically. This paper introduces our approach to proof planning, gives and overview of IsaPlanner, and presents one simple yet effective reasoning technique. 1
A rational reconstruction and extension of recursion analysis
 Proceedings of the Eleventh International Joint Conference on Artificial Intelligence
, 1989
"... The focus of this paper is the technique of recur8\on analysis. Recursion analysis is used by the BoyerMoore Theorem Prover to choose an appropriate induction schema and variable to prove theorems by mathematical induction. A rational reconstruction of recursion analysis is outlined, using the tech ..."
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Cited by 27 (14 self)
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The focus of this paper is the technique of recur8\on analysis. Recursion analysis is used by the BoyerMoore Theorem Prover to choose an appropriate induction schema and variable to prove theorems by mathematical induction. A rational reconstruction of recursion analysis is outlined, using the technique of proof plans. This rational reconstruction suggests an extension of recursion analysis which frees the induction suggestion from the forms of recursion found in the conjecture. Preliminary results are reported of the automation of this rational reconstruction and extension using the CLAMOyster system.
Analogy in Inductive Theorem Proving
, 1998
"... This paper investigates analogydriven proof plan construction in inductive theorem proving. We identify constraints of secondorder mappings that enable a replay of the plan of a source theorem to produce a similar plan for the target theorem. In some cases, differences between the source and ..."
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Cited by 25 (8 self)
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This paper investigates analogydriven proof plan construction in inductive theorem proving. We identify constraints of secondorder mappings that enable a replay of the plan of a source theorem to produce a similar plan for the target theorem. In some cases, differences between the source and target theorem mean that the target proof plan has to be reformulated. These reformulations are suggested by the mappings. The analogy procedure, implemented in ABALONE, is particularly useful for overriding the default control and suggesting lemmas. Employing analogy has extended the problem solving horizon of the proof planner CLAM : with analogy, some theorems could be proved that neither CLAM nor NQTHM could prove automatically.
The Use of Proof Plans to Sum Series
 11th Conference on Automated Deduction
, 1992
"... We describe a program for finding closed form solutions to finite sums. The program was built to test the applicability of the proof planning search control technique in a domain of mathematics outwith induction. This experiment was successful. The series summing program extends previous work in thi ..."
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Cited by 24 (15 self)
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We describe a program for finding closed form solutions to finite sums. The program was built to test the applicability of the proof planning search control technique in a domain of mathematics outwith induction. This experiment was successful. The series summing program extends previous work in this area and was built in a short time just by providing new series summing methods to our existing inductive theorem proving system Clam. One surprising discovery was the usefulness of the ripple tactic in summing series. Rippling is the key tactic for controlling inductive proofs, and was previously thought to be specialised to such proofs. However, it turns out to be the key subtactic used by all the main tactics for summing series. The only change required was that it had to be supplemented by a difference matching algorithm to set up some initial metalevel annotations to guide the rippling process. In inductive proofs these annotations are provided by the application of mathematical i...
The "Limit" Domain
 In
, 1998
"... Proof planning is an application of AIplanning in mathematical domains. As opposed to planning for domains such as blocks world or transportation, the domain knowledge for mathematical domains is dicult to extract. Hence proof planning requires clever knowledge engineering and representation ..."
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Cited by 20 (11 self)
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Proof planning is an application of AIplanning in mathematical domains. As opposed to planning for domains such as blocks world or transportation, the domain knowledge for mathematical domains is dicult to extract. Hence proof planning requires clever knowledge engineering and representation of the domain knowledge. We think that on the one hand, the resulting domain denitions that include operators, supermethods, controlrules, and constraint solver are interesting in itself. On the other hand, they can provide ideas for modeling other realistic domains and for means of search reduction in planning. Therefore, we present proof planning and an exemplary domain used for planning proofs of socalled limit theorems that lead to proofs that were beyond the capabilities of other current proof planners and theorem provers. 1 Introduction While humans can cope with long and complex proofs and have strategies to avoid less promising proof paths, classical automated theore...
An Adaptation of ProofPlanning to Declarer Play in Bridge
 IN BRIDGE. RESEARCH PAPER 575, DEPT. OF AI
, 1992
"... We present Finesse, a system that forms plans for declarer play in the game of Bridge. Finesse generalises the technique of proofplanning, developed at Edinburgh University in the context of mathematical theoremproving, to deal with the disjunctive choice encountered when planning under uncerta ..."
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Cited by 17 (11 self)
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We present Finesse, a system that forms plans for declarer play in the game of Bridge. Finesse generalises the technique of proofplanning, developed at Edinburgh University in the context of mathematical theoremproving, to deal with the disjunctive choice encountered when planning under uncertainty, and the contextdependency of actions produced by the presence of an opposition. In its domain of planning for individual suits, it correctly identified the proper lines of play found in many examples from the Bridge literature, supporting its decisions with probabilistic and qualitative information. Cases were even discovered in which Finesse revealed errors in the analyses presented by recognised authorities.
A Proof Planning Framework for Isabelle
, 2005
"... Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully ..."
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Cited by 14 (10 self)
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Proof planning is a paradigm for the automation of proof that focuses on encoding intelligence to guide the proof process. The idea is to capture common patterns of reasoning which can be used to derive abstract descriptions of proofs known as proof plans. These can then be executed to provide fully formal proofs. This thesis concerns the development and analysis of a novel approach to proof planning that focuses on an explicit representation of choices during search. We embody our approach as a proof planner for the generic proof assistant Isabelle and use the Isar language, which is humanreadable and machinecheckable, to represent proof plans. Within this framework we develop an inductive theorem prover as a case study of our approach to proof planning. Our prover uses the difference reduction heuristic known as rippling to automate the step cases of the inductive proofs. The development of a flexible approach to rippling that supports its various modifications and extensions is the second major focus of this thesis. Here, our inductive theorem prover provides a context in which to evaluate rippling experimentally. This work results in an efficient and powerful inductive theorem prover for Isabelle as well as proposals for further improving the efficiency of rippling. We also draw observations in order
Experiments in Automating Hardware Verification using Inductive Proof Planning
, 1996
"... We present a new approach to automating the verification of hardware designs based on planning techniques. A database of methods is developed that combines tactics, which construct proofs, using specifications of their behaviour. Given a verification problem, a planner uses the method database to ..."
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Cited by 13 (6 self)
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We present a new approach to automating the verification of hardware designs based on planning techniques. A database of methods is developed that combines tactics, which construct proofs, using specifications of their behaviour. Given a verification problem, a planner uses the method database to build automatically a specialised tactic to solve the given problem. User interaction is limited to specifying circuits and their properties and, in some cases, suggesting lemmas. We have implemented our work in an extension of the Clam proof planning system. We report on this and its application to verifying a variety of combinational and synchronous sequential circuits including a parameterised multiplier design and a simple computer microprocessor.
Using MiddleOut Reasoning to Control the Synthesis of TailRecursive Programs
 IN PROC. CADE11, LNAI 607
, 1992
"... We describe a novel technique for the automatic synthesis of tailrecursive programs. The technique is to specify the required program using the standard equations and then synthesise the tailrecursive program using the proofs as programs technique. This requires the specification to be proved r ..."
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Cited by 12 (5 self)
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We describe a novel technique for the automatic synthesis of tailrecursive programs. The technique is to specify the required program using the standard equations and then synthesise the tailrecursive program using the proofs as programs technique. This requires the specification to be proved realisable in a constructive logic. Restrictions on the form of the proof ensure that the synthesised program is tailrecursive. The
Proof Plans for the Correction of False Conjectures
 5TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING AND AUTOMATED REASONING, LPAR'94, LECTURE NOTES IN ARTIFICIAL INTELLIGENCE, V. 822
, 1994
"... Theorem proving is the systematic derivation of a mathematical proof from a set of axioms by the use of rules of inference. We are interested in a related but far less explored problem: the analysis and correction of false conjectures, especially where that correction involves finding a collection o ..."
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Cited by 11 (7 self)
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Theorem proving is the systematic derivation of a mathematical proof from a set of axioms by the use of rules of inference. We are interested in a related but far less explored problem: the analysis and correction of false conjectures, especially where that correction involves finding a collection of antecedents that, together with a set of axioms, transform nontheorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenomenon. Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct nontheorems.