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.
Proceedings of the ACM on Programming Languages 2(POPL), 23 (2017) 30 A
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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.