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System Description: Proof Planning in HigherOrder Logic with
 15th International Conference on Automated Deduction, volume 1421 of Lecture Notes in Artificial Intelligence
, 1998
"... Introduction Proof planning [4] is an approach to theorem proving which encodes heuristics for constructing mathematical proofs in a metatheory of methods. The Clam system, developed at Edinburgh [3], has been used for several years to develop proof planning, in particular proof plans for induction ..."
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Cited by 58 (8 self)
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Introduction Proof planning [4] is an approach to theorem proving which encodes heuristics for constructing mathematical proofs in a metatheory of methods. The Clam system, developed at Edinburgh [3], has been used for several years to develop proof planning, in particular proof plans for induction. It has become clear that many of the theoremproving tasks that we would like to perform are naturally higherorder. For example, an important technique called middleout reasoning [6] uses metavariables to stand for some unknown objects in a proof, to be instantiated as the proof proceeds. Domains such as the synthesis and verification of software and hardware systems, and techniques such as proof critics [7], benefit greatly from such middleout reasoning. Since in these domains the metavariables often become instantiated with terms of function type, reasoning with them is naturally higherorder, and higherorder unification is a
Proof Planning with Multiple Strategies
 In Proc. of the First International Conference on Computational Logic
, 2000
"... . Humans have different problem solving strategies at their disposal and they can flexibly employ several strategies when solving a complex problem, whereas previous theorem proving and planning systems typically employ a single strategy or a hard coded combination of a few strategies. We introd ..."
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Cited by 53 (34 self)
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. Humans have different problem solving strategies at their disposal and they can flexibly employ several strategies when solving a complex problem, whereas previous theorem proving and planning systems typically employ a single strategy or a hard coded combination of a few strategies. We introduce multistrategy proof planning that allows for combining a number of strategies and for switching flexibly between strategies in a proof planning process. Thereby proof planning becomes more robust since it does not necessarily fail if one problem solving mechanism fails. Rather it can reason about preference of strategies and about failures. Moreover, our strategies provide a means for structuring the vast amount of knowledge such that the planner can cope with the otherwise overwhelming knowledge in mathematics. 1 Introduction The choice of an appropriate problem solving strategy is a crucial human skill and is typically guided by some metalevel reasoning. Trained mathematicia...
A Calculus for and Termination of Rippling
 Journal of Automated Reasoning
, 1996
"... . Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general forma ..."
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Cited by 41 (2 self)
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. Rippling is a type of rewriting developed for inductive theorem proving that uses annotations to direct search. Rippling has many desirable properties: for example, it is highly goal directed, usually involves little search, and always terminates. In this paper we give a new and more general formalization of rippling. We introduce a simple calculus for rewriting annotated terms, close in spirit to firstorder rewriting, and prove that it has the formal properties desired of rippling. Next we develop criteria for proving the termination of such annotated rewriting, and introduce orders on annotated terms that lead to termination. In addition, we show how to make rippling more flexible by adapting the termination orders to the problem domain. Our work has practical as well as theoretical advantages: it has led to a very simple implementation of rippling that has been integrated in the Edinburgh CLAM system. Key words: Mathematical Induction, Inductive Theorem Proving, Term Rewriting. ...
ΩANTS  An open approach at combining Interactive and Automated Theorem Proving
 IN PROC. OF CALCULEMUS2000. AK PETERS
, 2000
"... We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integ ..."
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Cited by 35 (23 self)
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We present the ΩAnts theorem prover that is built on top of an agentbased command suggestion mechanism. The theorem prover inherits beneficial properties from the underlying suggestion mechanism such as runtime extendibility and resource adaptability. Moreover, it supports the distributed integration of external reasoning systems. We also introduce some notions that need to be considered to check completeness and soundness of such a system with respect to an underlying calculus.
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
Automated Theorem Proving by Test Set Induction
 Journal of Symbolic Computation
, 1997
"... Test set induction is a goaldirected proof technique which combines the full power of explicit induction and proof by consistency. It works by computing an appropriate explicit induction scheme called a test set, to trigger the induction proof, and then applies a refutation principle using proof by ..."
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Cited by 26 (10 self)
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Test set induction is a goaldirected proof technique which combines the full power of explicit induction and proof by consistency. It works by computing an appropriate explicit induction scheme called a test set, to trigger the induction proof, and then applies a refutation principle using proof by consistency techniques. We present a general scheme for test set induction together with a simple soundness proof. Our method is based on new notions of test sets, induction variables, and provable inconsistency, which allow us to refute false conjectures even in the case where the functions are not completely deøned. We show how test sets can be computed when the constructors are not free, and give an algorithm for computing induction variables. Finally, we present a procedure for proof by test set induction which is refutationally complete for a larger class of specifications than has been shown in previous work. The method has been implemented in the prover SPIKE. Based on computer ex...
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.
Invariant Discovery via Failed Proof Attempts
 In Proc. LOPSTR '98, LNCS 1559
, 1998
"... . We present a framework for automating the discovery of loop invariants based upon failed proof attempts. The discovery of suitable loop invariants represents a bottleneck for automatic verification of imperative programs. Using the proof planning framework we reconstruct standard heuristics fo ..."
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Cited by 18 (2 self)
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. We present a framework for automating the discovery of loop invariants based upon failed proof attempts. The discovery of suitable loop invariants represents a bottleneck for automatic verification of imperative programs. Using the proof planning framework we reconstruct standard heuristics for developing invariants. We relate these heuristics to the analysis of failed proof attempts allowing us to discover invariants through a process of refinement. 1 Introduction Loop invariants are a well understood technique for specifying the behaviour of programs involving loops. The discovery of suitable invariants, however, is a major bottleneck for automatic verification of imperative programs. Early research in this area [18, 24] exploited both theorem proving techniques as well as domain specific heuristics. However, the potential for interaction between these components was not fully exploited. The proof planning framework, in which we reconstruct the standard heuristics, couples ...
XBarnacle: Making Theorem Provers More Accessible
 14th International Conference on Automated Deduction
, 1997
"... Introduction XBarnacle was built to meet the challenge of incorporating interactive features in the automated theorem prover CLAM whilst preserving the advantages of automation. Many people are not able to use theorem provers to their full strength. The aim of our research is to make semiautomated ..."
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Cited by 15 (0 self)
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Introduction XBarnacle was built to meet the challenge of incorporating interactive features in the automated theorem prover CLAM whilst preserving the advantages of automation. Many people are not able to use theorem provers to their full strength. The aim of our research is to make semiautomated theorem proving a real possibility for a wide range of people  from those primarily interested in formal specification, for whom proof is a chore, to developers of automated theorem proving systems themselves. We give an account of the advantages and limitations of the CLAM proof planning system, and describe how XBarnacle, a semiautomatic theorem prover, enhances the capabilities of CLAM. 2 The CLAM theorem prover 2.1 Proof planning CLAM [3] is based on the notion of proof planning [2]. LCFstyle tactics  examples are induction, gene
Constructing induction rules for deductive synthesis proofs
 LFCS University of Edinburgh
, 2005
"... We describe novel computational techniques for constructing induction rules for deductive synthesis proofs. Deductive synthesis holds out the promise of automated construction of correct computer programs from specifications of their desired behaviour. Synthesis of programs with iteration or recursi ..."
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Cited by 15 (7 self)
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We describe novel computational techniques for constructing induction rules for deductive synthesis proofs. Deductive synthesis holds out the promise of automated construction of correct computer programs from specifications of their desired behaviour. Synthesis of programs with iteration or recursion requires inductive proof, but standard techniques for the construction of appropriate induction rules are restricted to recycling the recursive structure of the specifications. What is needed is induction rule construction techniques that can introduce novel recursive structures. We show that a combination of rippling and the use of metavariables as a leastcommitment device can provide such novelty. Key words: deductive synthesis, proof planning, induction, theorem proving, middleout reasoning. 1