BiSikkel: A Multimode Logical Framework in Agda

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 pr...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Proceedings of ACM on programming languages Ročník 9; číslo POPL; s. 210 - 240
Hlavní autoři: Ceulemans, Joris, Nuyts, Andreas, Devriese, Dominique
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY, USA ACM 07.01.2025
Témata:
Categorical semantics
Modal and temporal logics
Programming logic
Theory of computation
Type theory
Agda
presheaf semantics
multimode type theory (MTT)
ISSN:2475-1421, 2475-1421
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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:2475-1421
2475-1421
DOI:10.1145/3704844