research-article

Quantitative classical realizability

Author:

Aloïs BrunelAuthors Info & Claims

Information and Computation, Volume 241, Issue C

Pages 62 - 95

https://doi.org/10.1016/j.ic.2014.10.007

Published: 01 April 2015 Publication History

Abstract

Introduced by Dal Lago and Hofmann, quantitative realizability is a technique used to define models for logics based on Multiplicative Linear Logic. A particularity is that functions are interpreted as bounded time computable functions. It has been used to give new and uniform proofs of soundness of several type systems with respect to certain time complexity classes. We propose a reformulation of their ideas in the setting of Krivine's classical realizability. The framework obtained generalizes Dal Lago and Hofmann's realizability, and reveals deep connections between quantitative realizability and a linear variant of Cohen's forcing.

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Cited By

Hackett JHutton G(2018)Parametric polymorphism and operational improvementProceedings of the ACM on Programming Languages10.1145/32367632:ICFP(1-24)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3236763
Munch-Maccagnoni GScherer G(2015)Polarised Intermediate Representation of Lambda Calculus with SumsProceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2015.22(127-140)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/LICS.2015.22
Brunel AGaboardi MMazza DZdancewic S(2014)A Core Quantitative Coeffect CalculusProceedings of the 23rd European Symposium on Programming Languages and Systems - Volume 841010.1007/978-3-642-54833-8_19(351-370)Online publication date: 5-Apr-2014
https://dl.acm.org/doi/10.1007/978-3-642-54833-8_19

Quantitative classical realizability
1. Theory of computation
  1. Models of computation

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cover image Information and Computation

Information and Computation Volume 241, Issue C

April 2015

350 pages

ISSN:0890-5401

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Academic Press, Inc.

United States

Publication History

Published: 01 April 2015

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Cited By

Hackett JHutton G(2018)Parametric polymorphism and operational improvementProceedings of the ACM on Programming Languages10.1145/32367632:ICFP(1-24)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3236763
Munch-Maccagnoni GScherer G(2015)Polarised Intermediate Representation of Lambda Calculus with SumsProceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS.2015.22(127-140)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/LICS.2015.22
Brunel AGaboardi MMazza DZdancewic S(2014)A Core Quantitative Coeffect CalculusProceedings of the 23rd European Symposium on Programming Languages and Systems - Volume 841010.1007/978-3-642-54833-8_19(351-370)Online publication date: 5-Apr-2014
https://dl.acm.org/doi/10.1007/978-3-642-54833-8_19

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