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DOI: 10.4230/LIPIcs.CSL.2022.5

Gardening with the Pythia A Model of Continuity in a Dependent Setting

Authors: Martin Baillon, Assia Mahboubi, and Pierre-Marie Pédrot

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

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.

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Martin Baillon, Assia Mahboubi, and Pierre-Marie Pédrot. Gardening with the Pythia A Model of Continuity in a Dependent Setting. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@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/entities/document/10.4230/LIPIcs.CSL.2022.5},
  URN =		{urn:nbn:de:0030-drops-157256},
  doi =		{10.4230/LIPIcs.CSL.2022.5},
  annote =	{Keywords: Type theory, continuity, syntactic model}
}

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Gardening with the Pythia A Model of Continuity in a Dependent Setting

Abstract

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