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A proof of the Kepler conjecture
 Math. Intelligencer
, 1994
"... This section describes the structure of the proof of ..."
Abstract

Cited by 112 (11 self)
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This section describes the structure of the proof of
A proof of the dodecahedral conjecture
, 1998
"... This article gives a proof of Fejes Tóth’s Dodecahedral conjecture: the volume of a Voronoi polyhedron in a threedimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius. 1 ..."
Abstract

Cited by 5 (2 self)
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This article gives a proof of Fejes Tóth’s Dodecahedral conjecture: the volume of a Voronoi polyhedron in a threedimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius. 1
Verifying and Reasoning about Programs—Mechanical Verification
"... Sparse matrix formats are typically implemented with lowlevel imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variablefree functional language (LL) in which even advanced formats ..."
Abstract
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Sparse matrix formats are typically implemented with lowlevel imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variablefree functional language (LL) in which even advanced formats can be expressed naturally, as a pipelinestyle composition of smaller construction steps. We translate LL programs to Isabelle/HOL and describe a proof system based on parametric predicates for tracking relationship between mathematical vectors and their concrete representations. This proof theory automatically verifies full functional correctness of many formats. We show that it is reusable and extensible to hierarchical sparse formats. Categories and Subject Descriptors D.3.2 [Programming Languages]: Language Classifications—Specialized application languages;
Languages, Verification
"... Sparse matrix formats are typically implemented with lowlevel imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variablefree functional language (LL) in which even advanced formats ..."
Abstract
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Sparse matrix formats are typically implemented with lowlevel imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variablefree functional language (LL) in which even advanced formats can be expressed naturally, as a pipelinestyle composition of smaller construction steps. We translate LL programs to Isabelle/HOL and describe a proof system based on parametric predicates for tracking relationship between mathematical vectors and their concrete representations. This proof theory automatically verifies full functional correctness of many formats. We show that it is reusable and extensible to hierarchical sparse formats.