Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality · HackerPapers discussions

Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality — mentioned by omegafixedpoint

Sun, 07 Jun 2026 16:08:17 GMT

A few notes, because this is obviously vibe coded, and does not work in many ways. 1. Yon's documentation mentions "Homotopy type theory:" > the runnable HoTT fragment is refl/pair/fst/snd These are basic features of martin-lof type theory, not homotopy type theory. The documentation makes no reference of an interval type, which is generally the way to go for decidable type-checking in HoTT without univalence as an opaque axiom. Pi types are mentioned, but Yon does not have dependent types. From what I can tell, they are polymorphic, maybe even just simply-typed (except for identity types…

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Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality — mentioned by foooobar

Sat, 19 Jun 2021 20:18:22 GMT

Some constructivists may also take offense with proof irrelevance (and the resulting loss of normalization [1] or its incompatibility with HoTT), which you can only really avoid by avoiding Prop. [1] https://arxiv.org/abs/1911.08174

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Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality — mentioned by SkySkimmer

Tue, 28 Jan 2020 22:31:30 GMT

The normalization issue is not about quotients at all. It's https://arxiv.org/abs/1911.08174 "Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality"

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