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International Symposium on Logical Foundations of Computer Science

LFCS 2009: Logical Foundations of Computer Science pp 365–379Cite as

Unifying Sets and Programs via Dependent Types

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5407))

Abstract

We present a foundational framework, which we call D, unifying a lazy programming language with an impredicative constructive set theory IZF R by means of dependent types. We show that unification brings many benefits to both worlds. First, D supports two paramount paradigms of creating reliable software: correctness by construction and post-construction verification, while retaining the expressiveness of set theory. Second, D provides new expressive power, which makes it possible to internalize and prove inside D the standard meta-theoretic properties of constructive systems, such as Numerical Existence Property and Program Extraction. Finally, computation arising from the programming language significantly enriches set theory, as we show that D is stronger than IZF R and that its real numbers behave in a better way.

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Author information

Authors and Affiliations

  1. Google, New York, USA

    Wojciech Moczydłowski

Authors
  1. Wojciech Moczydłowski
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Editor information

Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, NY 10016, New York, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, NY 14853, Ithaca, USA

    Anil Nerode

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Moczydłowski, W. (2008). Unifying Sets and Programs via Dependent Types. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92687-0_25

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  • DOI: https://doi.org/10.1007/978-3-540-92687-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92686-3

  • Online ISBN: 978-3-540-92687-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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