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Extensional Universal Types for Call-by-Value

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Programming Languages and Systems (APLAS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5356))

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Abstract

We propose \({\lambda_{\text{c}}2_{\eta}}\) -calculus, which is a second-order polymorphic call-by-value calculus with extensional universal types. Unlike product types or function types in call-by-value, extensional universal types are genuinely right adjoint to the weakening, i.e., β-equality and η-equality hold for not only values but all terms. We give monadic style categorical semantics, so that the results can be applied also to languages like Haskell. To demonstrate validity of the calculus, we construct concrete models for the calculus in a generic manner, exploiting “relevant” parametricity. On such models, we can obtain a reasonable class of monads consistent with extensional universal types. This class admits polynomial-like constructions, and includes non-termination, exception, global state, input/output, and list-non-determinism.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Japan

    Kazuyuki Asada

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  1. Kazuyuki Asada
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Editors and Affiliations

  1. Microsoft Research India, 196/36, 2nd Main, Sadashivnagar, 560080, Bangalore, India

    G. Ramalingam

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Asada, K. (2008). Extensional Universal Types for Call-by-Value. In: Ramalingam, G. (eds) Programming Languages and Systems. APLAS 2008. Lecture Notes in Computer Science, vol 5356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89330-1_9

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  • DOI: https://doi.org/10.1007/978-3-540-89330-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89329-5

  • Online ISBN: 978-3-540-89330-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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