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A Universal Embedding for the Higher Order Structure of Computational Effects

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Typed Lambda Calculi and Applications (TLCA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2701))

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Abstract

We give a universal embedding of the semantics for the first order fragment of the computational λ-calculus into a semantics for the whole calculus. In category theoretic terms, which are the terms of the paper, this means we give a universal embedding of every small Freyd-category into a closed Freyd-category. The universal property characterises the embedding as the free completion of the Freyd-category as ca [→, Set]-enriched category under conical colimits. This embedding extends the usual Yoneda embedding of a small category with finite products into its free cocompletion, i.e., the usual category theoretic embedding of a model of the first order fragment of the simply typed λ-calculus into a model for the whole calculus, and similarly for the linear λ-calculus. It agrees with an embedding previously given in an ad hoc way without a universal property, so it shows the definitiveness of that construction.

This work is supported by AIST Japan, and by EPSRC grant GR/M56333: The structure of programming languages: syntax and semantics.

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Author information

Authors and Affiliations

  1. Laboratory for the Foundations of Computer Science, University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JZ, Scotland, UK

    John Power

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  1. John Power
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität München, Oettingenstr. 67, 80538, München, Germany

    Martin Hofmann

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© 2003 Springer-Verlag Berlin Heidelberg

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Power, J. (2003). A Universal Embedding for the Higher Order Structure of Computational Effects. In: Hofmann, M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44904-3_21

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  • DOI: https://doi.org/10.1007/3-540-44904-3_21

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40332-6

  • Online ISBN: 978-3-540-44904-1

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