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Linear Sized Types in the Calculus of Constructions

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Functional and Logic Programming (FLOPS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8475))

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Abstract

Sized types provide an expressive and compositional framework for proving termination and productivity of (co-)recursive definitions. In this paper, we study sized types with linear annotations of the form \(n·α+m\) with n and m natural numbers. Concretely, we present a type system with linear sized types for the Calculus of Constructions extended with one inductive type (natural numbers) and one coinductive type (streams). We show that this system satisfies desirable metatheoretical properties, including strong normalization, and give a sound and complete size-inference algorithm.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, USA

    Jorge Luis Sacchini

Authors
  1. Jorge Luis Sacchini
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer Sheva, Israel

    Michael Codish

  2. Graduate School of Information Sciences, Tohoku University, Aza-aoba 6-3-09, 980-8579, Sendai, Japan

    Eijiro Sumii

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Sacchini, J.L. (2014). Linear Sized Types in the Calculus of Constructions. In: Codish, M., Sumii, E. (eds) Functional and Logic Programming. FLOPS 2014. Lecture Notes in Computer Science, vol 8475. Springer, Cham. https://doi.org/10.1007/978-3-319-07151-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-07151-0_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07150-3

  • Online ISBN: 978-3-319-07151-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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