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Extracting a Normalization Algorithm in Isabelle/HOL

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Book cover Types for Proofs and Programs (TYPES 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3839))

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Abstract

We present a formalization of a constructive proof of weak normalization for the simply-typed λ-calculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. Unlike many other proofs of weak normalization based on Tait’s strong computability predicates, which require a logic supporting strong eliminations and can give rise to dependent types in the extracted program, our formalization requires only relatively simple proof principles. Thus, the program obtained from this proof is typable in simply-typed higher-order logic as implemented in Isabelle/HOL, and a proof of its correctness can automatically be derived within the system.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Stefan Berghofer

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  1. Stefan Berghofer
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Editor information

Editors and Affiliations

  1. LRI, Univ Paris-Sud, CNRS, Orsay F-91405, INRIA Futurs, ProVal, F-91893, Orsay

    Jean-Christophe Filliâtre

  2. INRIA Saclay - Île-de-France, ProVal - Orsay 91893 and LRI, Univ Paris-Sud, CNRS - Orsay 91405LRI, Université Paris Sud and INRIA Futurs, Bât. 490, Université Paris Sud, F-91405, Orsay Cedex, France

    Christine Paulin-Mohring

  3. INRIA-Futurs at, LIX, École Polytechnique, Palaiseau, France

    Benjamin Werner

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© 2006 Springer-Verlag Berlin Heidelberg

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Berghofer, S. (2006). Extracting a Normalization Algorithm in Isabelle/HOL. In: Filliâtre, JC., Paulin-Mohring, C., Werner, B. (eds) Types for Proofs and Programs. TYPES 2004. Lecture Notes in Computer Science, vol 3839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617990_4

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  • DOI: https://doi.org/10.1007/11617990_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31428-8

  • Online ISBN: 978-3-540-31429-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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