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Gardening with the Pythia A model of continuity in a dependent setting

Jardiner avec la Pythie

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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.
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Dates and versions

hal-03510671 , version 1 (04-01-2022)

Licence

Attribution - CC BY 4.0

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Martin Baillon, Assia Mahboubi, Pierre-Marie Pédrot. Gardening with the Pythia A model of continuity in a dependent setting. CSL 2022 - Computer Science Logic, Feb 2022, Göttingen, Germany. pp.1-19, ⟨10.4230/LIPIcs.CSL.2022.13⟩. ⟨hal-03510671⟩
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