Contravariant families in simplicial HoTT supply proof-relevant expansion, yielding directed Boolean canonicity and a binary parametricity model over reduction-aware syntax.
Logical Methods in Computer Science V olume 13, Issue 4 (Oct 2017)
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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.
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Directed proof-relevant logical relations in simplicial HoTT
Contravariant families in simplicial HoTT supply proof-relevant expansion, yielding directed Boolean canonicity and a binary parametricity model over reduction-aware syntax.
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Shallow Embedding of Type Theory is Morally Correct
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.