Type Theory in Type Theory using a Strictified Syntax
summary
They build an isomorphic, substitution strictified initial CwF that encodes substitutions as meta-level functions so all substitution equations become definitional, use categorical gluing and a contextualization/construction inside presheaf models, and then transport the induction principle back to prove canonicity for dependent products and booleans. The proof is fully formalised in Agda (artifacts available). Computation on the resulting syntax is bulky and some eliminator computation rules are lost, but the method avoids transport hell.
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