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Type theories can be formalized using the intrinsically (hard) or theextrinsically (soft) typed style. In large libraries of type theoreticalfeatures, often both styles are present, which can lead to code duplication andintegration issues.  We define an operator that systematically translates a hard-typed into thecorresponding soft-typed formulation. Even though this translation is known inprinciple, a number of subtleties make it more difficult than naively expected.Importantly, our translation preserves modularity, i.e., it maps structuredsets of hard-typed features to correspondingly structured soft-typed ones.  We implement our operator in the MMT system and apply it to a library oftype-theoretical features.

Systematic Translation of Formalizations of Type Theory from Intrinsic to Extrinsic Style