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

Florian Rabe
(University Erlangen-Nuremberg)
Navid Roux
(University Erlangen-Nuremberg)

Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration issues.

We define an operator that systematically translates a hard-typed into the corresponding soft-typed formulation. Even though this translation is known in principle, a number of subtleties make it more difficult than naively expected. Importantly, our translation preserves modularity, i.e., it maps structured sets of hard-typed features to correspondingly structured soft-typed ones.

We implement our operator in the MMT system and apply it to a library of type-theoretical features.

In Elaine Pimentel and Enrico Tassi: Proceedings Sixteenth Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2021), Pittsburgh, USA, 16th July 2021, Electronic Proceedings in Theoretical Computer Science 337, pp. 88–103.
Published: 16th July 2021.

ArXived at: bibtex PDF

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