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We present a model of type theory with dependent product, sum, and identity, in cubical sets. We describe a universe and explain how to transform an equivalence between two types into an equality. We also explain how to model propositional truncation and the circle. While not expressed internally in type theory, the model is expressed in a constructive… (More)

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)

- K Aamodt, B Abelev, A A Quintana, D Adamova, A M Adare, M M Aggarwal +494 others
- 2013

The first measurement of the charged-particle multiplicity density at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV is presented. For an event sample corresponding to the most central 5% of the hadronic cross section, the pseudorapidity density of primary charged particles at… (More)

- Simon Huber
- ArXiv
- 2016

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)

- K Aamodt, B Abelev, A Abrahantes Quintana, D Adamová, A M Adare, M M Aggarwal +494 others
- Physical review letters
- 2011

We report on the first measurement of the triangular v3, quadrangular v4, and pentagonal v5 charged particle flow in Pb-Pb collisions at sqrt(s(NN)) = 2.76 TeV measured with the ALICE detector at the CERN Large Hadron Collider. We show that the triangular flow can be described in terms of the initial spatial anisotropy and its fluctuations, which provides… (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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