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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 28 (9 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
Automata Based Symbolic Reasoning in Hardware Verification
, 1998
"... . We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L ad ..."
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Cited by 18 (11 self)
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. We present a new approach to hardware verification based on describing circuits in Monadic Secondorder Logic (M2L). We show how to use this logic to represent generic designs like nbit adders, which are parameterized in space, and sequential circuits, where time is an unbounded parameter. M2L admits a decision procedure, implemented in the Mona tool [17], which reduces formulas to canonical automata. The decision problem for M2L is nonelementary decidable and thus unlikely to be usable in practice. However, we have used Mona to automatically verify, or find errors in, a number of circuits studied in the literature. Previously published machine proofs of the same circuits are based on deduction and may involve substantial interaction with the user. Moreover, our approach is orders of magnitude faster for the examples considered. We show why the underlying computations are feasible and how our use of Mona generalizes standard BDDbased hardware reasoning. 1. Introduction Correctnes...
Higher order rippling in IsaPlanner
 Theorem Proving in Higher Order Logics 2004 (TPHOLs’04), LNCS 3223
, 2004
"... Abstract. We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner. We treat issues not previously examined, in particular regarding the existence of multiple annotations during rippling. This results in an efficient mechanism for rippling th ..."
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Cited by 15 (7 self)
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Abstract. We present an account of rippling with proof critics suitable for use in higher order logic in Isabelle/IsaPlanner. We treat issues not previously examined, in particular regarding the existence of multiple annotations during rippling. This results in an efficient mechanism for rippling that can conjecture and prove needed lemmas automatically as well as present the resulting proof plans as Isar style proof scripts. 1
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 13 (9 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
Predicate synthesis for correcting faulty conjectures: The proof planning paradigm
 Automated Software Engineering
, 2003
"... Departamento de ciencias computacionales ..."
Proof planning for firstorder temporal logic
 In proceedings of CADE, 20th International Conference on Automated Deduction
, 2005
"... Abstract. Proof planning is an automated reasoning technique which improves proof search by raising it to a metalevel. In this paper we apply proof planning to FirstOrder Linear Temporal Logic (FOLTL), which can be seen as a quantified version of Linear Temporal Logic, overcoming its finitary limi ..."
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Cited by 4 (3 self)
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Abstract. Proof planning is an automated reasoning technique which improves proof search by raising it to a metalevel. In this paper we apply proof planning to FirstOrder Linear Temporal Logic (FOLTL), which can be seen as a quantified version of Linear Temporal Logic, overcoming its finitary limitation. Automated reasoning in FOLTL is hard, since it is nonrecursively enumerable; but its expressiveness can be exploited to precisely model the behaviour of complex, infinitestate systems. In order to demonstrate the potentiality of our technique, we introduce a casestudy inspired by the Feature Interactions problem and we model it in FOLTL; we then describe a set of methods which tackle and solve the validation problem for a number of properties of the model; and lastly we present a set of experimental results showing that the methods we propose capture the common patterns in the proofs presented, guide the search at the object level and let the overall system build large and highly structured proofs. This paper to some extent improves over previous work that showed how proof planning can be used to detect such interactions. 1
Proof Planning Methods as Schemas
 J. Symbolic Computation
, 1999
"... A major problem in automated theorem proving is search control. Many expanded proofs are generally built from a large number of relatively lowlevel inference steps, with the results that searching the space of possible proofs at this level is very expensive. Proof planning is a technique by which c ..."
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Cited by 4 (0 self)
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A major problem in automated theorem proving is search control. Many expanded proofs are generally built from a large number of relatively lowlevel inference steps, with the results that searching the space of possible proofs at this level is very expensive. Proof planning is a technique by which common proof methods are encoded as schemas, which we call methods. Proofs built using methods tend to be short, because the methods encode relatively long sequences of inference steps, and to be understandable, because the user can recognise the mathematical techniques beeing applied. Proof critics exploit the highlevel nature of proof plans to patch the failed proof attempts. A mapping from proof planning methods and proof construction tactics provides a link between the proof planning metalevel and fully expansive (objectlevel) proofs. Extensive experiments with proof planning reveal that a knowledgebased approach to automating proof construction works, and has usefull properties.
Proofsearch in typetheoretic languages: an introduction
 Theoretical Computer Science
, 2000
"... We introduce the main concepts and problems in the theory of proofsearch in typetheoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proofsearch in typetheoretic languages; rather, we present som ..."
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Cited by 2 (1 self)
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We introduce the main concepts and problems in the theory of proofsearch in typetheoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proofsearch in typetheoretic languages; rather, we present some key ideas and problems, starting from wellmotivated points of departure such as a definition of a typetheoretic language or the relationship between languages and proofobjects. The strong connections between different proofsearch methods in logics, type theories and logical frameworks, together with their impact on programming and implementation issues, are central in this context.
BestFirst Rippling
, 2006
"... Rippling is a form of rewriting that guides search by only performing steps that reduce the syntactic differences between formulae. Termination is normally ensured by a measure that is decreases with each rewrite step. Because of this restriction, rippling will fail to prove theorems about, for exam ..."
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Cited by 2 (1 self)
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Rippling is a form of rewriting that guides search by only performing steps that reduce the syntactic differences between formulae. Termination is normally ensured by a measure that is decreases with each rewrite step. Because of this restriction, rippling will fail to prove theorems about, for example, mutual recursion as steps that temporarily increase the differences are necessary. Bestfirst rippling is an extension to rippling where the restrictions have been recast as heuristic scores for use in bestfirst search. If nothing better is available, previously illegal steps can be considered, making bestfirst rippling more flexible than ordinary rippling. We have implemented bestfirst rippling in the IsaPlanner system together with a mechanism for caching proofstates that helps remove symmetries in the search space, and machinery to ensure termination based on term embeddings. Our experiments show that the implementation of bestfirst rippling is faster on average than IsaPlanner’s version of traditional depthfirst rippling, and solves a range of problems where ordinary rippling fails.
Planning Equational Verification in CCS
 13th Conference on Automated Software Engineering, ASE’98
, 1998
"... Most efforts to automate formal verification of communicating systems have centred around finitestate systems (FSSs). However, FSSs are incapable of modelling many practical communicating systems and hence there is interest in a novel class of problems, which we call VIPS, involving valuepassing, ..."
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Cited by 1 (1 self)
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Most efforts to automate formal verification of communicating systems have centred around finitestate systems (FSSs). However, FSSs are incapable of modelling many practical communicating systems and hence there is interest in a novel class of problems, which we call VIPS, involving valuepassing, infinitestate, parameterised systems. Existing approaches using model checking over FSSs are insufficient for VIPSs, due to their inability both to reason with and about domainspecific theories, and to cope with systems having an unbounded or arbitrary state space. We use a Calculus of Communicating Systems (CCS) [13] with parameterised constants to express and specify VIPSs. We use the laws of CCS to conduct the verification task. This approach allows us to study communicating systems, regardless of their state space, and the data such systems communicate. Automating theorem proving in this system is an extremely difficult task. We provide automated methods for CCS analysis; they are ap...