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International Colloquium on Theoretical Aspects of Computing

ICTAC 2015: Theoretical Aspects of Computing - ICTAC 2015 pp 388–403Cite as

A Resource Aware Computational Interpretation for Herbelin’s Syntax

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9399))

Abstract

We investigate a new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics. For that, we associate to Herbelin’s syntax a type system based on non-idempotent intersection types, together with a set of reduction rules –inspired from the substitution at a distance paradigm– that preserves (and decreases the size of) typing derivations. The non-idempotent approach allows us to use very simple combinatorial arguments, only based on this measure decreasingness, to characterize strongly normalizing terms by means of typability. For the sake of completeness, we also study typability (and the corresponding strong normalization characterization) in the reduction calculus obtained from the former one by projecting the explicit substitutions.

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Notes

  1. 1.

    The node \(\mathtt{hlist}\) counts 2 since it corresponds, in the standard sequent calculus, to an application of an axiom rule followed by a contraction.

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Author information

Authors and Affiliations

  1. University Paris-Diderot, SPC, PPS, CNRS, Paris, France

    Delia Kesner

  2. University Federal de Goiás, INF, Goiânia, Brazil

    Daniel Ventura

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  1. Delia Kesner
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  2. Daniel Ventura
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Correspondence to Daniel Ventura .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Schleswig-Holstein, Germany

    Martin Leucker

  2. Pontificia Universidad Javeriana-Cali, Cali, Colombia

    Camilo Rueda

  3. Pontificia Universidad Javeriana-Cali, CNRS LIX École Polytechnique de Paris, Palaiseau Cedex, France

    Frank D. Valencia

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Kesner, D., Ventura, D. (2015). A Resource Aware Computational Interpretation for Herbelin’s Syntax. In: Leucker, M., Rueda, C., Valencia, F. (eds) Theoretical Aspects of Computing - ICTAC 2015. ICTAC 2015. Lecture Notes in Computer Science(), vol 9399. Springer, Cham. https://doi.org/10.1007/978-3-319-25150-9_23

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  • DOI: https://doi.org/10.1007/978-3-319-25150-9_23

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