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44
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 29 (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.
Automatic Synthesis of Recursive Programs: The ProofPlanning Paradigm
, 1997
"... We describe a proof plan that characterises a family of proofs corresponding to the synthesis of recursive functional programs. This plan provides a significant degree of automation in the construction of recursive programs from specifications, together with correctness proofs. This plan makes use o ..."
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Cited by 23 (2 self)
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We describe a proof plan that characterises a family of proofs corresponding to the synthesis of recursive functional programs. This plan provides a significant degree of automation in the construction of recursive programs from specifications, together with correctness proofs. This plan makes use of metavariables to allow successive refinement of the identity of unknowns, and so allows the program and the proof to be developed hand in hand. We illustrate the plan with parts of a substantial example  the synthesis of a unification algorithm.
Higherorder Annotated Terms for Proof Search
 THEOREM PROVING IN HIGHER ORDER LOGICS: 9TH INTERNATIONAL CONFERENCE, TPHOLS’96
, 1996
"... A notion of embedding appropriate to higherorder syntax is described. This provides a representation of annotated formulae in terms of the difference between pairs of formulae. We define substitution and unification for such annotated terms. Using this representation of annotated terms, the proof s ..."
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Cited by 21 (3 self)
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A notion of embedding appropriate to higherorder syntax is described. This provides a representation of annotated formulae in terms of the difference between pairs of formulae. We define substitution and unification for such annotated terms. Using this representation of annotated terms, the proof search guidance technique of rippling can be extended to higherorder theorems. We illustrate this by several examples based on an implementation of these ideas in Prolog.
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 19 (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 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 16 (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.
On the Automatic Discovery of Loop Invariants
, 1997
"... We present a technique for automating the discovery of loop invariants based upon the analysis of failed proof attempts. Previously we have shown how failure analysis may be used productively in the search for inductive proofs. This work had direct application to the verification of functional progr ..."
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Cited by 15 (4 self)
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We present a technique for automating the discovery of loop invariants based upon the analysis of failed proof attempts. Previously we have shown how failure analysis may be used productively in the search for inductive proofs. This work had direct application to the verification of functional programs. Here we show how these ideas can also play an important role in the formal verification of imperative programs. While presented as an automatic technique we believe that our approach may be easily integrated within an interactive proof environment.
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 14 (7 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.
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
A MultiLevel Approach to program Synthesis
, 1998
"... We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results ..."
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Cited by 13 (9 self)
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We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results achieved in the course of this development.