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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 ..."
Abstract

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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.
An Integration of Mechanised Reasoning Computer Algebra that Respects Explicit Proofs
, 1996
"... Mechanised reasoning systems and computer algebra systems have apparently different objectives. Their integration is, however, highly desirable, since in many formal proofs both of the two different tasks, proving and calculating, have to be performed. Even more importantly, proof and computation ..."
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Mechanised reasoning systems and computer algebra systems have apparently different objectives. Their integration is, however, highly desirable, since in many formal proofs both of the two different tasks, proving and calculating, have to be performed. Even more importantly, proof and computation are often interwoven and not easily separable. In the context of producing reliable proofs, the question how to ensure correctness when integrating a computer algebra system into a mechanised reasoning system is crucial. In this contribution, we discuss the correctness problems that arise from such an integration and advocate an approach in which the calculations of the computer algebra system are checked at the calculus level of the mechanised reasoning system. This can be achieved by adding a verbose mode to the computer algebra system which produces highlevel protocol information that can be processed by an interface to derive proof plans. Such a proof plan in turn can be expan...