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BiSikkel: A Multimode Logical Framework in Agda

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Názov: BiSikkel: A Multimode Logical Framework in Agda
Autori: Ceulemans, Joris, Nuyts, Andreas, Devriese, Dominique
Zdroj: Proceedings of the ACM on Programming Languages. 9:210-240
Informácie o vydavateľovi: Association for Computing Machinery (ACM), 2025.
Rok vydania: 2025
Predmety: 4613 Theory of computation, 4903 Numerical and computational mathematics, 4612 Software engineering
Popis: Embedding Multimode Type Theory (MTT) as a library enables the usage of additional reasoning principles in off-the-shelf proof assistants without risking soundness or compatibility. Moreover, by interpreting embedded MTT terms in an internally constructed model of MTT, we can extract programs and proofs to the metalanguage and obtain interoperability between the embedded language and the metalanguage. The existing Sikkel library for Agda achieves this for Multimode Simple Type Theory (MSTT) with an internal presheaf model of dependent MTT. In this work, we add, on top of the simply-typed layer, a logical framework in which users can write multimode proofs about multimode Sikkel programs, still in an off-the-shelf proof assistant. To this end, we carve out of MTT a new multimode logical framework µLF over MSTT and implement it on top of Sikkel, interpreting both in the existing internal model. In the process, we further extend and improve the original codebase for each of the three layers (syntax, semantics and extraction) of Sikkel. We demonstrate the use of µLF by proving some properties about functions manipulating guarded streams and by implementing an example involving parametricity predicates.
Druh dokumentu: Article
Jazyk: English
ISSN: 2475-1421
DOI: 10.1145/3704844
Rights: CC BY
Prístupové číslo: edsair.doi.dedup.....6f74f6179e636f8335fe25bd502b636f
Databáza: OpenAIRE
Popis
Abstrakt:Embedding Multimode Type Theory (MTT) as a library enables the usage of additional reasoning principles in off-the-shelf proof assistants without risking soundness or compatibility. Moreover, by interpreting embedded MTT terms in an internally constructed model of MTT, we can extract programs and proofs to the metalanguage and obtain interoperability between the embedded language and the metalanguage. The existing Sikkel library for Agda achieves this for Multimode Simple Type Theory (MSTT) with an internal presheaf model of dependent MTT. In this work, we add, on top of the simply-typed layer, a logical framework in which users can write multimode proofs about multimode Sikkel programs, still in an off-the-shelf proof assistant. To this end, we carve out of MTT a new multimode logical framework µLF over MSTT and implement it on top of Sikkel, interpreting both in the existing internal model. In the process, we further extend and improve the original codebase for each of the three layers (syntax, semantics and extraction) of Sikkel. We demonstrate the use of µLF by proving some properties about functions manipulating guarded streams and by implementing an example involving parametricity predicates.
ISSN:24751421
DOI:10.1145/3704844