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DOI: 10.4230/LIPIcs.CSL.2022.5
URN: urn:nbn:de:0030-drops-157256
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15725/
Baillon, Martin ; Mahboubi, Assia ; Pédrot, Pierre-Marie
Gardening with the Pythia A Model of Continuity in a Dependent Setting
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Abstract
We generalize to a rich dependent type theory a proof originally developed by Escardó that all System 𝚃 functionals are continuous. It relies on the definition of a syntactic model of Baclofen Type Theory, a type theory where dependent elimination must be strict, into the Calculus of Inductive Constructions. The model is given by three translations: the axiom translation, that adds an oracle to the context; the branching translation, based on the dialogue monad, turning every type into a tree; and finally, a layer of algebraic binary parametricity, binding together the two translations. In the resulting type theory, every function f : (ℕ → ℕ) → ℕ is externally continuous.
BibTeX - Entry
@InProceedings{baillon_et_al:LIPIcs.CSL.2022.5,
author = {Baillon, Martin and Mahboubi, Assia and P\'{e}drot, Pierre-Marie},
title = {{Gardening with the Pythia A Model of Continuity in a Dependent Setting}},
booktitle = {30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
pages = {5:1--5:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-218-1},
ISSN = {1868-8969},
year = {2022},
volume = {216},
editor = {Manea, Florin and Simpson, Alex},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/15725},
URN = {urn:nbn:de:0030-drops-157256},
doi = {10.4230/LIPIcs.CSL.2022.5},
annote = {Keywords: Type theory, continuity, syntactic model}
}
| Keywords: | Type theory, continuity, syntactic model | |
| Seminar: | 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 27.01.2022 | |
| Supplementary Material: | Software (Source Code): https://gitlab.inria.fr/mbaillon/gardening-with-the-pythia archived at: https://archive.softwareheritage.org/swh:1:dir:0cb62da6eae2909b912bdf29e37e9b0e6875ff52 |
