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Higher order functions in first order logics

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Theory of Computing and Systems (ISTCS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 601))

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Abstract

Most of approaches to extracting programs from (constructive) proofs use type theories. Usually it is argued that first order logic has many drawbacks to be used as a language for programming in logic. In particular, higher order functions are not directly expressible in first order logic. Here we show how to use proof schemes in first order logic for representing higher order functions. We generalize the semantics introduced in [Vor 90] to the proof schemes and show how it is related to extraction of higher order functions from proofs in first order logic.

On leave from the International Laboratory of Intelligent Systems (SINTEL), 630090, Universitetski Prospect 4, Novosibirsk 90, Russia (voronkov@sintel.nsk.su).

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Authors and Affiliations

  1. ECRC, Arabellastr. 17, 8000, Munich 81, Germany

    Andrei Voronkov

Authors
  1. Andrei Voronkov
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Editor information

D. Dolev Z. Galil M. Rodeh

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© 1992 Springer-Verlag Berlin Heidelberg

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Voronkov, A. (1992). Higher order functions in first order logics. In: Dolev, D., Galil, Z., Rodeh, M. (eds) Theory of Computing and Systems. ISTCS 1992. Lecture Notes in Computer Science, vol 601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035165

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  • DOI: https://doi.org/10.1007/BFb0035165

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55553-7

  • Online ISBN: 978-3-540-47214-8

  • eBook Packages: Springer Book Archive

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