Article

Non-idempotent Intersection Types in Logical Form

Author:

Thomas EhrhardAuthors Info & Claims

Foundations of Software Science and Computation Structures: 23rd International Conference, FOSSACS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, Proceedings

Pages 198 - 216

https://doi.org/10.1007/978-3-030-45231-5_11

Published: 25 April 2020 Publication History

Abstract

Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the evaluation of terms and programs. However, unlike simple or second-order types, intersection types cannot be considered as a logical system because the application rule (or the intersection rule, depending on the presentation of the system) involves a condition stipulating that the proofs of premises must have the same structure. Using earlier work introducing an indexed version of Linear Logic, we show that non-idempotent typing can be given a logical form in a system where formulas represent hereditarily indexed families of intersection types.

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Cited By

Ke WChan K(2021)A Subtyping Scheme for Nominal and Structural Types Based on Class Graph EquivalenceProceedings of the 2021 4th International Conference on Blockchain Technology and Applications10.1145/3510487.3510509(151-157)Online publication date: 17-Dec-2021
https://dl.acm.org/doi/10.1145/3510487.3510509

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Non-idempotent Intersection Types in Logical Form

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Published In

cover image Guide Proceedings

Foundations of Software Science and Computation Structures: 23rd International Conference, FOSSACS 2020, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020, Dublin, Ireland, April 25–30, 2020, Proceedings

Apr 2020

656 pages

ISBN:978-3-030-45230-8

DOI:10.1007/978-3-030-45231-5

Editors:
Jean Goubault-Larrecq
ENS/CNRS, Université Paris-Saclay, Cachan, France
,
Barbara König
University of Duisburg-Essen, Duisburg, Germany

© The Author(s) 2020.

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 25 April 2020

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Cited By

Ke WChan K(2021)A Subtyping Scheme for Nominal and Structural Types Based on Class Graph EquivalenceProceedings of the 2021 4th International Conference on Blockchain Technology and Applications10.1145/3510487.3510509(151-157)Online publication date: 17-Dec-2021
https://dl.acm.org/doi/10.1145/3510487.3510509

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