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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)
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)
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)
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)
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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