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Three non-cubical applications of extension types

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arxiv 2311.05658 v2 pith:AO73D5FV submitted 2023-11-09 cs.PL

Tesla Zhang This is my paper · ORCID
classification cs.PL
keywords typeapplicationstheorycubicalextensiontypesarticlebeen
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The development of cubical type theory inspired the idea of "extension types" which has been found to have applications in other type theories that are unrelated to homotopy type theory or cubical type theory. This article describes these applications, including on records, metaprogramming, controlling unfolding, and some more exotic ones.

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  1. Extension Types for Free

    cs.LO 2026-07 accept novelty 8.0 of 10 full

    Extension types are definable in two-level type theory, all their Riehl–Shulman rules become theorems, and cubical gluing is equivalent to univalence in this framework.

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