1 Search Results for "Ong, C.-H. Luke"

Document
DOI: 10.4230/LIPIcs.FSCD.2020.32
The Difference λ-Calculus: A Language for Difference Categories

Authors: Mario Alvarez-Picallo and C.-H. Luke Ong

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

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.
Cite as

Mario Alvarez-Picallo and C.-H. Luke Ong. The Difference λ-Calculus: A Language for Difference Categories. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{alvarezpicallo_et_al:LIPIcs.FSCD.2020.32,
  author =	{Alvarez-Picallo, Mario and Ong, C.-H. Luke},
  title =	{{The Difference \lambda-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 =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.32},
  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}
}
  • Refine by Author
  • 1 Alvarez-Picallo, Mario
  • 1 Ong, C.-H. Luke

  • Refine by Classification
  • 1 Theory of computation → Categorical semantics
  • 1 Theory of computation → Lambda calculus
  • 1 Theory of computation → Type theory

  • Refine by Keyword
  • 1 Cartesian difference categories
  • 1 Cartesian differential categories
  • 1 Change actions
  • 1 Difference lambda-calculus
  • 1 Differential lambda-calculus

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2020

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact