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Calculational Reasoning Revisited  An Isabelle/Isar experience
 THEOREM PROVING IN HIGHER ORDER LOGICS: TPHOLS 2001
, 2001
"... We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for highlevel natural deduction proofs that may be written in a humanreadable fashion. Setting out from a few basic logical concepts of the underlying metalogical framework of Isabelle, such ..."
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Cited by 14 (5 self)
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We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for highlevel natural deduction proofs that may be written in a humanreadable fashion. Setting out from a few basic logical concepts of the underlying metalogical framework of Isabelle, such as higherorder unification and resolution, calculational commands are added to the basic Isar proof language in a flexible and nonintrusive manner. Thus calculational proof style may be combined with the remaining natural deduction proof language in a liberal manner, resulting in many useful proof patterns. A casestudy on formalizing Computational Tree Logic (CTL) in simplytyped settheory demonstrates common calculational idioms in practice.
ComputerAssisted Mathematics at Work  The HahnBanach Theorem in Isabelle/Isar
 TYPES FOR PROOFS AND PROGRAMS: TYPESâ€™99, LNCS
, 2000
"... We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides ..."
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Cited by 7 (4 self)
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We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for highlevel reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
The layers of Logiweb
 In Kauers et al. [11
"... Abstract. Logiweb is an open source, distributed system for publication of machine checked mathematics. It covers all aspects of electronic publishing: high typographical quality, archival, handling of references to previously published results, and publication of refereed volumes. The present paper ..."
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Cited by 6 (0 self)
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Abstract. Logiweb is an open source, distributed system for publication of machine checked mathematics. It covers all aspects of electronic publishing: high typographical quality, archival, handling of references to previously published results, and publication of refereed volumes. The present paper is itself produced using Logiweb; and the paper is formally correct in the sense that it has been verified by Logiweb. The paper describes the implementation layers of the Logiweb system as seen by the user: the programming layer, the metalogic layer, the tactic layer, and the object proof layer. 1
Logiweb  a system for web publication of mathematics
 In Mathematical Software  ICMS 2006
, 2006
"... Abstract. Logiweb is a system for electronic publication and archival of machine checked mathematics of high typographic quality. It can verify the formal correctness of pages, i.e. mathematical papers expressed suitably. The present paper is an example of such a Logiweb page and the present paper i ..."
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Cited by 2 (1 self)
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Abstract. Logiweb is a system for electronic publication and archival of machine checked mathematics of high typographic quality. It can verify the formal correctness of pages, i.e. mathematical papers expressed suitably. The present paper is an example of such a Logiweb page and the present paper is formally correct in the sense that it has been verified by Logiweb. The paper may of course contain informal errors like any other paper. Logiweb is neutral with respect to choice of logic and choice of notation and can support any kind of formal reasoning. Logiweb uses the World Wide Web to publish Logiweb pages and Logiweb pages can be viewed by ordinary Web browsers. Logiweb pages can reference definitions, lemmas, and proofs on previously referenced Logiweb pages across the Internet. When Logiweb verifies a Logiweb page, it takes all transitively referenced pages into account. 1