REDUCTION FREE NORMALIZATION FOR A PROOF-IRRELEVANT TYPE OF PROPOSITIONS

Journal article, 2023

We show normalization for a type theory with a hierarchy of universes and a proof irrelevant type of propositions, close to the type system used in the proof assistant Lean. The proof uses the technique of Artin glueing between the term model and a suitable preseaf model. This can also be seen as a proof relevant version of Tait's computability argument.