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A Coalgebraic Foundation for Coinductive Union Types

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Automata, Languages, and Programming (ICALP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8573))

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Abstract

This paper introduces a coalgebraic foundation for coinductive types, interpreted as sets of values and extended with set theoretic union. We give a sound and complete characterization of semantic subtyping in terms of inclusion of maximal traces. Further, we provide a technique for reducing subtyping to inclusion between sets of finite traces, based on approximation. We obtain inclusion of tree languages as a sound and complete method to show semantic subtyping of recursive types with basic types, product and union, interpreted coinductively.

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Author information

Authors and Affiliations

  1. LIACS — Leiden University, The Netherlands

    Marcello Bonsangue, Jurriaan Rot & Frank de Boer

  2. Formal Methods — Centrum Wiskunde en Informatica, The Netherlands

    Marcello Bonsangue, Jurriaan Rot, Frank de Boer & Jan Rutten

  3. DIBRIS — Universita di Genova, Italy

    Davide Ancona

  4. ICIS — Radboud University Nijmegen, The Netherlands

    Jan Rutten

Authors
  1. Marcello Bonsangue
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  2. Jurriaan Rot
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  3. Davide Ancona
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  4. Frank de Boer
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  5. Jan Rutten
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstrasse 3, 85748, München, Germany

    Javier Esparza

  2. LIAFA, Université Paris Diderot-Paris 7, Case 7014, 75205, Paris Cedex 13, France

    Pierre Fraigniaud

  3. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Thore Husfeldt

  4. Department Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK,

    Elias Koutsoupias

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Bonsangue, M., Rot, J., Ancona, D., de Boer, F., Rutten, J. (2014). A Coalgebraic Foundation for Coinductive Union Types. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_6

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  • DOI: https://doi.org/10.1007/978-3-662-43951-7_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43950-0

  • Online ISBN: 978-3-662-43951-7

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