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.2020.32
URN: urn:nbn:de:0030-drops-123549
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12354/
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Alvarez-Picallo, Mario ; Ong, C.-H. Luke

The Difference λ-Calculus: A Language for Difference Categories

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LIPIcs-FSCD-2020-32.pdf (0.6 MB)

Abstract

Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only "up to an infinitesimal perturbation". In this work, we construct a simply-typed calculus in the spirit of the differential λ-calculus equipped with syntactic "infinitesimals" and show how its models correspond to difference λ-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials.

BibTeX - Entry

@InProceedings{alvarezpicallo_et_al:LIPIcs:2020:12354,
  author =	{Mario Alvarez-Picallo and C.-H. Luke Ong},
  title =	{{The Difference λ-Calculus: A Language for Difference Categories}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{32:1--32:21},
  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/2020/12354},
  URN =		{urn:nbn:de:0030-drops-123549},
  doi =		{10.4230/LIPIcs.FSCD.2020.32},
  annote =	{Keywords: Cartesian difference categories, Cartesian differential categories, Change actions, Differential lambda-calculus, Difference lambda-calculus}
}

Keywords: Cartesian difference categories, Cartesian differential categories, Change actions, Differential lambda-calculus, Difference lambda-calculus
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020

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