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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
Assisted proof document authoring
 Mathematical Knowledge Management MKM 2005, LNAI 3863
, 2006
"... Abstract. Recently, significant advances have been made in formalised mathematical texts for large, demanding proofs. But although such large developments are possible, they still take an inordinate amount of effort and time, and there is a significant gap between the resulting formalised machinech ..."
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Cited by 10 (3 self)
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Abstract. Recently, significant advances have been made in formalised mathematical texts for large, demanding proofs. But although such large developments are possible, they still take an inordinate amount of effort and time, and there is a significant gap between the resulting formalised machinecheckable proof scripts and the corresponding humanreadable mathematical texts. We present an authoring system for formal proof which addresses these concerns. It is based on a central document format which, in the tradition of literate programming, allows one to extract either a formal proof script or a humanreadable document; the two may have differing structure and detail levels, but are developed together in a synchronised way. Additionally, we introduce ways to assist production of the central document, by allowing tools to contribute backflow to update and extend it. Our authoring system builds on the new PG Kit architecture for Proof General, bringing the extra advantage that it works in a uniform interface, generically across various interactive theorem provers. 1
A DocumentOriented Coq Plugin for TEXmacs
, 2006
"... This article discusses the integration of the authoring of a mathematical document with the formalisation of the mathematics contained in that document. To achieve this we have started the development of a Coq plugin for the TEXmacs scientific editor, called tmEgg. TEXmacs allows the wysiwyg editing ..."
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Cited by 5 (4 self)
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This article discusses the integration of the authoring of a mathematical document with the formalisation of the mathematics contained in that document. To achieve this we have started the development of a Coq plugin for the TEXmacs scientific editor, called tmEgg. TEXmacs allows the wysiwyg editing of mathematical documents, much in the style of LATEX. Our plugin allows to integrate into a TEXmacs document mathematics formalised in the Coq proof assistant: formal definitions, lemmas and proofs. The plugin is still under development. Its main current hallmark is a documentconsistent interaction model, instead of the calculatorlike approach usual for TEXmacs plugins. This means that the Coq code in the TEXmacs document is interpreted as one (consistent) Coq file: executing a Coq command in the document means to execute it in the context (state) of all the Coq commands before it. 1
Structured induction proofs in Isabelle/Isar
 MATHEMATICAL KNOWLEDGE MANAGEMENT (MKM 2006), LNAI
, 2006
"... Isabelle/Isar is a generic framework for humanreadable formal proof documents, based on higherorder natural deduction. The Isar proof language provides general principles that may be instantiated to particular objectlogics and applications. We discuss specific Isar language elements that support ..."
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Cited by 4 (1 self)
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Isabelle/Isar is a generic framework for humanreadable formal proof documents, based on higherorder natural deduction. The Isar proof language provides general principles that may be instantiated to particular objectlogics and applications. We discuss specific Isar language elements that support complex induction patterns of practical importance. Despite the additional bookkeeping required for induction with local facts and parameters, definitions, simultaneous goals and multiple rules, the resulting Isar proof texts turn out wellstructured and readable. Our techniques can be applied to nonstandard variants of induction as well, such as coinduction and nominal induction. This demonstrates that Isar provides a viable platform for building domainspecific tools that support fullyformal mathematical proof composition.