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Infinite Intersection and Union Types for the Lazy Lambda Calculus

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Theoretical Aspects of Computer Software (TACS 2001)

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Abstract

A type theory with infinitary intersection and union types for the lazy λ-calculus is introduced. Types are viewed as upper closed subsets of a Scott domain. Intersection and union type constructors are interpreted as the set-theoretic intersection and union, respectively, even when they are not finite. The assignment of types to λ-terms extends naturally the basic type assignment system. We prove soundness and completeness using a generalization of Abramsky’s finitary domain logic for applicative transition systems.

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Author information

Authors and Affiliations

  1. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Marcello M. Bonsangue & Joost N. Kok

Authors
  1. Marcello M. Bonsangue
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  2. Joost N. Kok
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Editors and Affiliations

  1. Department of Computer Science, Tokyo Institute of Technology Graduate School of Information Science and Engineering, 2-12-1 Oo-okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Naoki Kobayashi

  2. Department of Computer and Information Science, University of Pennsylvania, 200 S. 33rd St., Philadelphia, PA, 19104, USA

    Benjamin C. Pierce

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Bonsangue, M.M., Kok, J.N. (2001). Infinite Intersection and Union Types for the Lazy Lambda Calculus. In: Kobayashi, N., Pierce, B.C. (eds) Theoretical Aspects of Computer Software. TACS 2001. Lecture Notes in Computer Science, vol 2215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45500-0_22

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  • DOI: https://doi.org/10.1007/3-540-45500-0_22

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  • Print ISBN: 978-3-540-42736-0

  • Online ISBN: 978-3-540-45500-4

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