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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)
Obtaining homogenous aspartyl-containing peptides via Fmoc/tBu chemistry is often an insurmountable obstacle. A generic solution for this issue utilising an optimised side-chain protection strategy that minimises aspartimide formation would therefore be most desirable. To this end, we developed the following new derivatives: Fmoc-Asp(OEpe)-OH (Epe =(More)
Laboratory for Photonics and Interfaces, Institute of Chemical Sciences and Engineering, School of Basic Sciences, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland, Laboratory for Functional Polymers, Empa, Swiss Federal Laboratories for Materials Testing and Research, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland, and Istituto CNR(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)
The controlled fabrication of submicrometer phase-separated morphologies of semiconducting organic materials is attracting considerable interest, for example, in emerging thin-film optoelectronic device applications. For thin films of spin-coated blends of PCBM ([6,6]-phenyl-C 61-butyric acid methyl ester) and cationic cyanine dyes, we used atomic force(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)
In our efforts to develop a universal solution to the problem of aspartimide formation in Fmoc SPPS, we investigated the application of our new β-trialkylmethyl protected aspartic acid building blocks to the synthesis of peptides containing the Asp-Gly motif. The N(α)-Fmoc aspartic acid β-tri-(ethyl/propyl/butyl)methyl esters were used in the synthesis of(More)
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