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The Structural λ-Calculus

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Computer Science Logic (CSL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6247))

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Abstract

Inspired by a recent graphical formalism for λ-calculus based on Linear Logic technology, we introduce an untyped structural λ-calculus, called λj, which combines action at a distance with exponential rules decomposing the substitution by means of weakening, contraction and dereliction. Firstly, we prove fundamental properties such as confluence and preservation of β-strong normalisation. Secondly, we use λj to describe known notions of developments and superdevelopments, and introduce a more general one called XL-development. Then we show how to reformulate Regnier’s σ-equivalence in λj so that it becomes a strong bisimulation. Finally, we prove that explicit composition or de-composition of substitutions can be added to λj while still preserving β-strong normalisation.

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Author information

Authors and Affiliations

  1. PPS (CNRS and Université Paris Diderot),  

    Beniamino Accattoli & Delia Kesner

Authors
  1. Beniamino Accattoli
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  2. Delia Kesner
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Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Formal Methods in Systems Engineering, Vienna University of Technology, Favoritenstr. 9-11, 1040, Vienna, Austria

    Helmut Veith

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Accattoli, B., Kesner, D. (2010). The Structural λ-Calculus. In: Dawar, A., Veith, H. (eds) Computer Science Logic. CSL 2010. Lecture Notes in Computer Science, vol 6247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15205-4_30

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  • DOI: https://doi.org/10.1007/978-3-642-15205-4_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15204-7

  • Online ISBN: 978-3-642-15205-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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