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Intuitive and Formal Representations: The Case of Matrices
 In MKM’04, LNCS 3119
, 2004
"... A major obstacle for bridging the gap between textbook mathematics and formalising it on a computer is the problem how to adequately capture the intuition inherent in the mathematical notation when formalising mathematical concepts. While logic is an excellent tool to represent certain mathemati ..."
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Cited by 8 (3 self)
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A major obstacle for bridging the gap between textbook mathematics and formalising it on a computer is the problem how to adequately capture the intuition inherent in the mathematical notation when formalising mathematical concepts. While logic is an excellent tool to represent certain mathematical concepts it often fails to retain all the information implicitly given in the representation of some mathematical objects. In this paper we concern ourselves with matrices, whose representation can be particularly rich in implicit information. We analyse dierent types of matrices and present a mechanism that can represent them very close to their textbook style appearance and captures the information contained in this representation but that nevertheless allows for their compilation into a formal logical framework. This rstly allows for a more humanoriented interface and secondly enables ecient reasoning with matrices.
Computer Theorem Proving in Math
"... We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. ..."
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We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context.
An Idealistic Formalization of Stokes’ Theorem: Pedagogical Math in Isabelle/ISAR
"... In this thesis, we describe the trials and tribulations of an attempt to formalize the ndimensional version of Stokes ’ theorem, aka the fundamental theorem of multivariate calculus, in Isabelle/HOL. A fundamental goal of this development was to obtain textbookstyle readable proofs that would be ..."
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In this thesis, we describe the trials and tribulations of an attempt to formalize the ndimensional version of Stokes ’ theorem, aka the fundamental theorem of multivariate calculus, in Isabelle/HOL. A fundamental goal of this development was to obtain textbookstyle readable proofs that would be reusable by future proof developers. We analyze the nature of modularity in mathematics and compare it to Isabelle’s programmatic support for modularism. We also present an extension to Isabelle that manages predicate subtype information transparently. Finally, we let the proofs themselves tell their mathematical story, with commentary on their design process. iii Acknowledgements Many thanks to all of the dreamers of Edinburgh, who put up with me for an entire summer. Extra special thanks to Lucas Dixon, for being an Isabelle superstar, Robbert Brak, for adding some inconsistency to my academic life, and Jacques Fleuriot, without whose enthusiastic oversight, none of this would have been possible.
unknown title
, 2004
"... Abstract: We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical settheoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in revision, and also contains as a tara ..."
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Abstract: We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical settheoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in revision, and also contains as a tarattachment to the source file the revised and expanded version of the proof development which had been attached to math.HO/0311260.