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This paper presents a type theory in which it is possible to directly manipulate n-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways to reason about identity types, for instance, function extensionality is directly provable in the system. Further,(More)
Objective. To assess the effect of spinal cord stimulation in patients with severe, inoperable peripheral vascular disease, and uncontrolled pain. Patients and methods. A case study of 20 patients with end-stage peripheral vascular disease, either Fontaine Class 3 or 4 limb ischemia. All 20 patients implanted with spinal cord stimulation devices with(More)
Dye-sensitized solar cells (DSSCs) have attracted significant attention as low-cost alternatives to conventional solid-state pho-tovoltaic devices. 1-3 In these cells, the most successful charge-transfer sensitizers employed are ruthenium polypyridyl complexes, yielding 9-11% solar-to-electric power conversion efficiencies under AM 1.5. 4 The majority of(More)
Cubical type theory is an extension of Martin-Löf type theory recently proposed by Cohen, Coquand, Mörtberg and the author which allows for direct manipulation of n-dimensional cubes and where Voevodsky's Univalence Axiom is provable. In this paper we prove canonicity for cubical type theory: any natural number in a context build from only name variables is(More)
OBJECTIVES Donation after circulatory declaration of death (DCDD) could significantly improve the number of cardiac grafts for transplantation. Graft evaluation is particularly important in the setting of DCDD given that conditions of cardio-circulatory arrest and warm ischaemia differ, leading to variable tissue injury. The aim of this study was to(More)
We present an interpretation of a version of dependent type theory where a type is interpreted by a Kan semisimplicial set. This interprets only a weak notion of conversion similar to the one used in the first published version of Martin-Löf type theory. Each truncated version of this model can be carried out internally in dependent type theory, and we have(More)
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