Contravariant families in simplicial HoTT supply proof-relevant expansion, yielding directed Boolean canonicity and a binary parametricity model over reduction-aware syntax.
Normalization by gluing for free {\lambda}-theories
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abstract
The connection between normalization by evaluation, logical predicates and semantic gluing constructions is a matter of folklore, worked out in varying degrees within the literature. In this note, we present an elementary version of the gluing technique which corresponds closely with both semantic normalization proofs and the syntactic normalization by evaluation.
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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.