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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2022.5
URN: urn:nbn:de:0030-drops-157256
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15725/
Baillon, Martin ;
Mahboubi, Assia ;
Pédrot, Pierre-Marie
Gardening with the Pythia A Model of Continuity in a Dependent Setting
Abstract
We generalize to a rich dependent type theory a proof originally developed by Escardó that all System ? 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}
}
