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We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further sho...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.400.9250 2023-05-15T14:49:52+02:00 Contents Christian Sternagel René Thiemann The Pennsylvania State University CiteSeerX Archives 2013 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.9250 http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.9250 http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf text 2013 ftciteseerx 2016-01-08T02:48:37Z We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic semirings satisfy the axioms that are required by our matrix theory. Our formalization was performed as part of the IsaFoR/CeTA-system [3] 1 which contains several termination techniques. The provided theories have been essential to formalize matrix-interpretations [1] and arctic interpretations [2]. A short description of this formalization can be found in [4]. Text Arctic Unknown Arctic |
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We provide the operations of matrix addition, multiplication, transposition, and matrix comparisons as executable functions over ordered semirings. Moreover, it is proven that strongly normalizing (monotone) orders can be lifted to strongly normalizing (monotone) orders over matrices. We further show that the standard semirings over the naturals, integers, and rationals, as well as the arctic semirings satisfy the axioms that are required by our matrix theory. Our formalization was performed as part of the IsaFoR/CeTA-system [3] 1 which contains several termination techniques. The provided theories have been essential to formalize matrix-interpretations [1] and arctic interpretations [2]. A short description of this formalization can be found in [4]. |
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The Pennsylvania State University CiteSeerX Archives |
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Christian Sternagel René Thiemann |
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Christian Sternagel René Thiemann Contents |
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Christian Sternagel René Thiemann |
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Christian Sternagel |
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2013 |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.9250 http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf |
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http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.9250 http://afp.sourceforge.net/browser_info/current/HOL/Matrix/document.pdf |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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