| Title: |
Gardening with the Pythia A Model of Continuity in a Dependent Setting |
| Authors: |
Baillon, Martin; Mahboubi, Assia; Pédrot, Pierre-Marie |
| Contributors: |
Martin Baillon and Assia Mahboubi and Pierre-Marie Pédrot |
| Publisher Information: |
Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Publication Year: |
2022 |
| Collection: |
DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Subject Terms: |
Type theory; continuity; syntactic model |
| Description: |
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. |
| Document Type: |
article in journal/newspaper; conference object |
| File Description: |
application/pdf |
| Language: |
English |
| Relation: |
Is Part Of LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.5 |
| DOI: |
10.4230/LIPIcs.CSL.2022.5 |
| Availability: |
https://doi.org/10.4230/LIPIcs.CSL.2022.5; https://nbn-resolving.org/urn:nbn:de:0030-drops-157256; https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.5 |
| Rights: |
https://creativecommons.org/licenses/by/4.0/legalcode |
| Accession Number: |
edsbas.2ECFBC16 |
| Database: |
BASE |