[2308.08404] A topological counterpart of well-founded trees in dependent type theory
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Computer Science > Logic in Computer Science

arXiv:2308.08404 (cs)
[Submitted on 16 Aug 2023 (v1), last revised 22 Nov 2023 (this version, v2)]

Title:A topological counterpart of well-founded trees in dependent type theory

Authors:Maria Emilia Maietti, Pietro Sabelli
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Abstract:Within dependent type theory, we provide a topological counterpart of well-founded trees (for short, W-types) by using a proof-relevant version of the notion of inductively generated suplattices introduced in the context of formal topology under the name of inductively generated basic covers. In more detail, we show, firstly, that in Homotopy Type Theory, W-types and proof relevant inductively generated basic covers are propositionally mutually encodable. Secondly, we prove they are definitionally mutually encodable in the Agda implementation of intensional Martin-Loef's type theory. Finally, we reframe the equivalence in the Minimalist Foundation framework by introducing well-founded predicates as the logical counterpart for predicates of dependent W-types. All the results have been checked in the Agda proof-assistant.
Comments: To be published in the post-proceedings of the 39th Conference on Mathematical Foundations of Programming Semantics
Subjects: Logic in Computer Science (cs.LO)
ACM classes: F.4.1
Cite as: arXiv:2308.08404 [cs.LO]
  (or arXiv:2308.08404v2 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2308.08404
Journal reference: Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:11755
Related DOI: https://doi.org/10.46298/entics.11755

Submission history

From: Michael Mislove [view email]
[v1] Wed, 16 Aug 2023 14:48:09 UTC (44 KB)
[v2] Wed, 22 Nov 2023 15:41:15 UTC (221 KB)
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