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Interpolation for Natural Deduction with Generalized Eliminations

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Proof Theory in Computer Science (PTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2183))

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Abstract

A modification of simply-typed λ-calculus by generalized elimination rules in the style of von Plato is presented. Its characteristic feature are permutative conversions also for function types and product types. After the addition of certain extensional reduction rules, an interpolation theorem (à la Lyndon) is proven which is also aware of the terms (a. k. a. the proofs via the Curry-Howard-isomorphism) like in Čubrić’s treatment of the usual λ-calculus. Connections between interpolation and canonical liftings of positive and negative type dependencies are given which are important for the intensional treatment of inductive datatypes.

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References

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Author information

Authors and Affiliations

  1. Institut für Informatik der Ludwig-Maximilians-Universität München, Oettingenstraße 67, D-80538, München, Germany

    Ralph Matthes

Authors
  1. Ralph Matthes
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Editor information

Editors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Reinhard Kahle  & Peter Schroeder-Heister  & 

  2. Theoretische Informatik, ETH Zürich, ETH Zentrum, 8092, Zürich, Switzerland

    Robert Stärk

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© 2001 Springer-Verlag Berlin Heidelberg

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Matthes, R. (2001). Interpolation for Natural Deduction with Generalized Eliminations. In: Kahle, R., Schroeder-Heister, P., Stärk, R. (eds) Proof Theory in Computer Science. PTCS 2001. Lecture Notes in Computer Science, vol 2183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45504-3_10

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  • DOI: https://doi.org/10.1007/3-540-45504-3_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42752-0

  • Online ISBN: 978-3-540-45504-2

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