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.CSL.2021.25
URN: urn:nbn:de:0030-drops-134592
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13459/
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Guerrieri, Giulio ; Olimpieri, Federico

Categorifying Non-Idempotent Intersection Types

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LIPIcs-CSL-2021-25.pdf (0.7 MB)

Abstract

Non-idempotent intersection types can be seen as a syntactic presentation of a well-known denotational semantics for the lambda-calculus, the category of sets and relations. Building on previous work, we present a categorification of this line of thought in the framework of the bang calculus, an untyped version of Levy’s call-by-push-value. We define a bicategorical model for the bang calculus, whose syntactic counterpart is a suitable category of types. In the framework of distributors, we introduce intersection type distributors, a bicategorical proof relevant refinement of relational semantics. Finally, we prove that intersection type distributors characterize normalization at depth 0.

BibTeX - Entry

@InProceedings{guerrieri_et_al:LIPIcs:2021:13459,
  author =	{Giulio Guerrieri and Federico Olimpieri},
  title =	{{Categorifying Non-Idempotent Intersection Types}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{25:1--25:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Christel Baier and Jean Goubault-Larrecq},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13459},
  URN =		{urn:nbn:de:0030-drops-134592},
  doi =		{10.4230/LIPIcs.CSL.2021.25},
  annote =	{Keywords: Linear logic, bang calculus, non-idempotent intersection types, distributors, relational semantics, combinatorial species, symmetric sequences, bicategory, categorification}
}

Keywords: Linear logic, bang calculus, non-idempotent intersection types, distributors, relational semantics, combinatorial species, symmetric sequences, bicategory, categorification
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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