Abstract
AbstractThis article presents Trocq, a new proof transfer framework for dependent type theory. Trocq is based on a novel formulation of type equivalence, used to generalize the univalent parametricity translation. This framework takes care of avoiding dependency on the axiom of univalence when possible, and may be used with more relations than just equivalences. We have implemented a corresponding plugin for the interactive theorem prover, in the meta-language.
Publisher
Springer Nature Switzerland
Reference35 articles.
1. The lean mathematical library. In: Blanchette, J., Hritcu, C. (eds.) Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2020, New Orleans, LA, USA, January 20-21, 2020. pp. 367–381. ACM (2020). https://doi.org/10.1145/3372885.3373824, https://doi.org/10.1145/3372885.3373824
2. Affeldt, R., Cohen, C.: Measure construction by extension in dependent type theory with application to integration (2023), accepted for publication in JAR
3. Altenkirch, T., Kaposi, A.: Towards a cubical type theory without an interval. In: TYPES. LIPIcs, vol. 69, pp. 3:1–3:27. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)
4. Angiuli, C., Brunerie, G., Coquand, T., Harper, R., (Favonia), K.H., Licata, D.R.: Syntax and models of cartesian cubical type theory. Math. Struct. Comput. Sci. 31(4), 424–468 (2021). https://doi.org/10.1017/S0960129521000347, https://doi.org/10.1017/S0960129521000347
5. Angiuli, C., Cavallo, E., Mörtberg, A., Zeuner, M.: Internalizing representation independence with univalence. Proc. ACM Program. Lang. 5(POPL), 1–30 (2021). https://doi.org/10.1145/3434293, https://doi.org/10.1145/3434293
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