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Not Enough Points Is Enough

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Computer Science Logic (CSL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4646))

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Abstract

Models of the untyped λ-calculus may be defined either as applicative structures satisfying a bunch of first-order axioms (λ-models), or as reflexive objects in cartesian closed categories (categorical models). In this paper we show that any categorical model of λ-calculus can be presented as a λ-model, even when the underlying category does not have enough points. We provide an example of an extensional model of λ-calculus in a category of sets and relations which has not enough points. Finally, we present some of its algebraic properties which make it suitable for dealing with non-deterministic extensions of λ-calculus.

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Authors and Affiliations

  1. Laboratoire PPS, CNRS UMR 7126-Université Paris 7, 2, place Jussieu (case 7014), 75251 Paris Cedex 05, France

    Antonio Bucciarelli, Thomas Ehrhard & Giulio Manzonetto

  2. Institut de Mathématiques de Luminy CNRS UMR 6206, 163, avenue de Luminy, case 907 13288 Marseille, France

    Thomas Ehrhard

  3. Università Ca’Foscari di Venezia, Dipartimento di Informatica, Via Torino 155, 30172 Venezia, Italia

    Giulio Manzonetto

Authors
  1. Antonio Bucciarelli
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  2. Thomas Ehrhard
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  3. Giulio Manzonetto
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Jacques Duparc Thomas A. Henzinger

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Bucciarelli, A., Ehrhard, T., Manzonetto, G. (2007). Not Enough Points Is Enough. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_24

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  • DOI: https://doi.org/10.1007/978-3-540-74915-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74914-1

  • Online ISBN: 978-3-540-74915-8

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