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

Authors Martin Baillon, Assia Mahboubi, Pierre-Marie Pédrot

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Martin Baillon
  • INRIA and LS2N, Nantes, France
Assia Mahboubi
  • INRIA and LS2N, Nantes, France
Pierre-Marie Pédrot
  • INRIA and LS2N, Nantes, France

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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)
https://doi.org/10.4230/LIPIcs.CSL.2022.5

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
Keywords
  • Type theory
  • continuity
  • syntactic model

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