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CGRASS: A System for Transforming Constraint Satisfaction Problems
 Recent Advances in Constraints, 1530, LNCS 2627
, 2002
"... Abstract. Experts at modelling constraint satisfaction problems (CSPs) carefully choose model transformations to reduce greatly the amount of effort that is required to solve a problem by systematic search. It is a considerable challenge to automate such transformations and to identify which transfo ..."
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Cited by 26 (9 self)
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Abstract. Experts at modelling constraint satisfaction problems (CSPs) carefully choose model transformations to reduce greatly the amount of effort that is required to solve a problem by systematic search. It is a considerable challenge to automate such transformations and to identify which transformations are useful. Transformations include adding constraints that are implied by other constraints, adding constraints that eliminate symmetrical solutions, removing redundant constraints and replacing constraints with their logical equivalents. This paper describes the CGRASS (Constraint Generation And Symmetrybreaking) system that can improve a problem model by automatically performing transformations of these kinds. We focus here on transforming individual CSP instances. Experiments on the Golomb ruler problem suggest that producing good problem formulations solely by transforming problem instances is, generally, infeasible. We argue that, in certain cases, it is better to transform the problem class than individual instances and, furthermore, it can sometimes be better to transform formulations of a problem that are more abstract than a CSP. 1
Proof Planning
 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON AI PLANNING SYSTEMS, (AIPS
, 1996
"... We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans cons ..."
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Cited by 24 (2 self)
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We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans constructed by plan formation techniques. Some differences are the nonpersistence of objects in the mathematical domain, the absence of goal interaction in mathematics, the high degree of generality of proof plans, the use of a metalogic to describe preconditions in proof planning and the use of annotations in formulae to guide search.
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
A survey of automated deduction
 EDINBURGH ARTI INTELLIGENCE RESEARCH PAPER 950
, 1999
"... We survey research in the automation of deductive inference, from its beginnings in the early history of computing to the present day. We identify and describe the major areas of research interest and their applications. The area is characterised by its wide variety of proof methods, forms of autom ..."
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Cited by 12 (0 self)
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We survey research in the automation of deductive inference, from its beginnings in the early history of computing to the present day. We identify and describe the major areas of research interest and their applications. The area is characterised by its wide variety of proof methods, forms of automated deduction and applications.
Change of Representation in Theorem Proving by Analogy
, 1993
"... Constructing an analogy between a known and already proven theorem (the base case) and another yet to be proven theorem (the target case) often amounts to finding the appropriate representation at which the base and the target are similar. This is a wellknown fact in mathematics, and it was corrobo ..."
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Cited by 11 (9 self)
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Constructing an analogy between a known and already proven theorem (the base case) and another yet to be proven theorem (the target case) often amounts to finding the appropriate representation at which the base and the target are similar. This is a wellknown fact in mathematics, and it was corroborated by our empirical study of a mathematical textbook, which showed that a reformulation of the representation of a theorem and its proof is indeed more often than not a necessary prerequisite for an analogical inference. Thus machine supported reformulation becomes an important component of automated analogydriven theorem proving too. The reformulation component proposed in this paper is embedded into a proof plan methodology based on methods and metamethods, where the latter are used to change and appropriately adapt the methods. A theorem and its proof are both represented as a method and then reformulated by the set of metamethods presented in this paper. Our approach supports analog...
Extensions to Proof Planning for Generating Implied Constraints
 In Proceedings of Calculemus01
, 2001
"... . We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about al ..."
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Cited by 11 (7 self)
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. We describe how proof planning is being extended to generate implied algebraic constraints. This inference problem introduces a number of challenging problems like deciding a termination condition and evaluating constraint utility. We have implemented a number of methods for reasoning about algebraic constraints. For example, the eliminate method performs Gaussianlike elimination of variables and terms. We are also reusing proof methods from the PRESS equation solving system like (variable) isolation. 1
Transforming and refining abstract constraint specifications
 In Proceedings of the Sixth Symposium on Abstraction, Reformulation and Approximation, volume 3607 of Lecture Notes in Computer Science
, 2005
"... ..."
Using a Generalisation Critic to Find Bisimulations for Coinductive Proofs
 PROCEEDINGS OF THE 14TH CONFERENCE ON AUTOMATED DEDUCTION, VOLUME 1249 OF LECTURE NOTES IN ARTIFICIAL INTELIGENCE
, 1997
"... Coinduction is a method of growing importance in reasoning about functional languages, due to the increasing prominence of lazy data structures. Through the use of bisimulations and proofs that observational equivalence is a congruence in various domains it can be used to proof the congruence of ..."
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Cited by 11 (2 self)
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Coinduction is a method of growing importance in reasoning about functional languages, due to the increasing prominence of lazy data structures. Through the use of bisimulations and proofs that observational equivalence is a congruence in various domains it can be used to proof the congruence of two processes. Several proof tools have been developed to aid coinductive proofs but all require user interaction. Crucially they require the user to supply an appropriate relation which the system can then prove to be a bisimulation. A method is proposed which uses the idea of proof plans to make a heuristic guess at a suitable relation. If the proof fails for that relation the reasons for failure are analysed using a proof critic and a new relation is proposed to allow the proof to go through.
DECLARE: A Prototype Declarative Proof System for Higher Order Logic
, 1997
"... This report describes DECLARE, a prototype implementation of a declarative proof system for simple higher order logic. The purpose of DECLARE is to explore mechanisms of specification and proof that may be incorporated into other theorem provers. It has been developed to aid with reasoning about ope ..."
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Cited by 10 (1 self)
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This report describes DECLARE, a prototype implementation of a declarative proof system for simple higher order logic. The purpose of DECLARE is to explore mechanisms of specification and proof that may be incorporated into other theorem provers. It has been developed to aid with reasoning about operational descriptions of systems and languages. Proofs in DECLARE are expressed as proof outlines, in a language that approximates written mathematics. The proof language includes specialised constructs for (co)inductive types and relations. The system includes an abstract/article mechanism that provides a way of isolating the process of formalization from what results, and simultaneously allow the efficient separate processing of work units. After describing the system we discuss our approach to two subsidiary issues: automation and the interactive environment provided to the user. 1 Introduction This technical report describes DECLARE, a prototype implementation of a declarative proof sy...