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arxiv: 1810.09367 · v1 · pith:J44LYO6Snew · submitted 2018-10-22 · 💻 cs.PL

Canonicity and normalisation for Dependent Type Theory

classification 💻 cs.PL
keywords typecanonicitydependentnotionreducibilitytheoryapproachargument
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We show canonicity and normalization for dependent type theory with a cumulative sequence of universes and a type of Boolean. The argument follows the usual notion of reducibility, going back to Godel's Dialectica interpretation and the work of Tait. A key feature of our approach is the use of a proof relevant notion of reducibility.

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  1. Shallow Embedding of Type Theory is Morally Correct

    cs.LO 2019-07 unverdicted novelty 6.0

    Shallow embedding of type theory into Agda is injective up to definitional equality via a syntactic translation model, with implementation hiding ensuring no illegal propositional equalities arise.