License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2020.25
URN: urn:nbn:de:0030-drops-123472
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12347/
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Xu, Chuangjie

A Gentzen-Style Monadic Translation of Gödel’s System T

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LIPIcs-FSCD-2020-25.pdf (0.5 MB)


Abstract

We introduce a syntactic translation of Gödel’s System 𝖳 parametrized by a weak notion of a monad, and prove a corresponding fundamental theorem of logical relation. Our translation structurally corresponds to Gentzen’s negative translation of classical logic. By instantiating the monad and the logical relation, we reveal the well-known properties and structures of 𝖳-definable functionals including majorizability, continuity and bar recursion. Our development has been formalized in the Agda proof assistant.

BibTeX - Entry

@InProceedings{xu:LIPIcs:2020:12347,
  author =	{Chuangjie Xu},
  title =	{{A Gentzen-Style Monadic Translation of G{\"o}del’s System T}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Zena M. Ariola},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12347},
  URN =		{urn:nbn:de:0030-drops-123472},
  doi =		{10.4230/LIPIcs.FSCD.2020.25},
  annote =	{Keywords: monadic translation, G{\"o}del’s System T, logical relation, negative translation, majorizability, continuity, bar recursion, Agda}
}

Keywords: monadic translation, Gödel’s System T, logical relation, negative translation, majorizability, continuity, bar recursion, Agda
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020
Supplementary Material: Agda development: https://github.com/cj-xu/GentzenTrans


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