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.2021.24
URN: urn:nbn:de:0030-drops-134586
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Guerrieri, Giulio ; Heijltjes, Willem B. ; Paulus, Joseph W.N.

A Deep Quantitative Type System

LIPIcs-CSL-2021-24.pdf (0.6 MB)


We investigate intersection types and resource lambda-calculus in deep-inference proof theory. We give a unified type system that is parametric in various aspects: it encompasses resource calculi, intersection-typed lambda-calculus, and simply-typed lambda-calculus; it accommodates both idempotence and non-idempotence; it characterizes strong and weak normalization; and it does so while allowing a range of algebraic laws to determine reduction behaviour, for various quantitative effects. We give a parametric resource calculus with explicit sharing, the "collection calculus", as a Curry-Howard interpretation of the type system, that embodies these computational properties.

BibTeX - Entry

  author =	{Giulio Guerrieri and Willem B. Heijltjes and Joseph W.N. Paulus},
  title =	{{A Deep Quantitative Type System}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{24:1--24:24},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-134586},
  doi =		{10.4230/LIPIcs.CSL.2021.24},
  annote =	{Keywords: Lambda-calculus, Deep inference, Intersection types, Resource calculus}

Keywords: Lambda-calculus, Deep inference, Intersection types, Resource calculus
Collection: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)
Issue Date: 2021
Date of publication: 13.01.2021

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