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The Power of Linear Functions

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Computer Science Logic (CSL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4207))

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Abstract

The linear lambda calculus is very weak in terms of expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with Booleans, natural numbers and a linear iterator. We show properties of this linear version of Gödel’s System \(\mathcal{T}\) and study the class of functions that can be represented. Surprisingly, this linear calculus is extremely expressive: it is as powerful as System \(\mathcal{T}\)

Research partially supported by the Treaty of Windsor Grant: “Linearity: Programming Languages and Implementations”, and by funds granted to LIACC through the Programa de Financiamento Plurianual, FCT and FEDER/POSI.

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Authors and Affiliations

  1. Department of Computer Science & LIACC, University of Porto, R. do Campo Alegre 823, 4150-180, Porto, Portugal

    Sandra Alves & Mário Florido

  2. Department of Computer Science, King’s College London, Strand, London, WC2R 2LS, U.K.

    Maribel Fernández & Ian Mackie

  3. LIX, École Polytechnique, 91128 Cedex, Palaiseau, France

    Ian Mackie

Authors
  1. Sandra Alves
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  2. Maribel Fernández
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  3. Mário Florido
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  4. Ian Mackie
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Zoltán Ésik

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© 2006 Springer-Verlag Berlin Heidelberg

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Alves, S., Fernández, M., Florido, M., Mackie, I. (2006). The Power of Linear Functions. In: Ésik, Z. (eds) Computer Science Logic. CSL 2006. Lecture Notes in Computer Science, vol 4207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11874683_8

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  • DOI: https://doi.org/10.1007/11874683_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45458-8

  • Online ISBN: 978-3-540-45459-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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