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  <article articleNo="27">
    <title>Encoding Tight Typing in a Unified Framework</title>
    <abstract>This paper explores how the intersection type theories of call-by-name (CBN) and call-by-value (CBV) can be unified in a more general framework provided by call-by-push-value (CBPV). Indeed, we propose tight type systems for CBN and CBV that can be both encoded in a unique tight type system for CBPV. All such systems are quantitative, i.e. they provide exact information about the length of normalization sequences to normal form as well as the size of these normal forms. Moreover, the length of reduction sequences are discriminated according to their multiplicative and exponential nature, a concept inherited from linear logic. Last but not least, it is possible to extract quantitative measures for CBN and CBV from their corresponding encodings in CBPV.</abstract>
    <keyword>Call-by-Push-Value</keyword>
    <keyword>Call-by-Name</keyword>
    <keyword>Call-by-Value</keyword>
    <keyword>Intersection Types</keyword>
    <subjectClassification acmID="10003752">Theory of computation</subjectClassification>
    <pages>27:1-27:20</pages>
    <category>Regular Paper</category>
    <funding>This work has been partially supported by IRP SINFIN.</funding>
    <relatedVersions>
      <url description="Full Version">https://arxiv.org/abs/2105.00564</url>
    </relatedVersions>
    <acknowledgements>We are specially grateful to G. Guerrieri for fruitful discussions. We also thank B. Accattoli, A. Bucciarelli, and A. Ríos for constructive remarks.</acknowledgements>
    <author>
      <firstName>Delia</firstName>
      <lastName>Kesner</lastName>
      <name>Delia Kesner</name>
      <affiliation>Université de Paris, CNRS, IRIF, France</affiliation>
      <affiliation>Institut Universitaire de France (IUF), France</affiliation>
      <homepageUrl/>
      <orcid>https://orcid.org/0000-0003-4254-3129</orcid>
    </author>
    <author>
      <firstName>Andrés</firstName>
      <lastName>Viso</lastName>
      <name>Andrés Viso</name>
      <affiliation>Inria, Paris, France</affiliation>
      <homepageUrl/>
      <orcid>https://orcid.org/0000-0002-6822-8453</orcid>
    </author>
    <doi>10.4230/LIPIcs.CSL.2022.27</doi>
    <contentUrl/>
    <archivedUrl/>
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    <copyright>Delia Kesner and Andrés Viso</copyright>
    <license>Creative Commons Attribution 4.0 International license</license>
    <licenseUrl>https://creativecommons.org/licenses/by/4.0/legalcode</licenseUrl>
    <publishedAt>2022-01-27</publishedAt>
  </article>
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