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Extracting General Recursive Program Schemes in Nuprl’s Type Theory

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Logic Based Program Synthesis and Transformation (LOPSTR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2372))

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Abstract

Nuprl supports program synthesis by extracting programs from proofs. In this paper we describe the extraction of “efficient” recursion schemes from proofs of well-founded induction principles. This is part of a larger methodology; when these well-founded induction principles are used in proofs, the structure of the program extracted from the proof is determined by the recursion scheme inhabiting the induction principle. Our development is based on Paulson’s paper Constructing recursion operators in intuitionistic type theory, but we specifically address two possibilities raised in the conclusion of his paper: the elimination of non-computational content from the recursion schemes themselves and, the use of the Y combinator to allow the recursion schemes to be extracted directly from the proofs of well-founded relations.

This research was supported by NSF CCR-9985239

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Authors and Affiliations

  1. Department of Computer Science, University of Wyoming, Laramie Wyoming

    James L. Caldwell

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  1. James L. Caldwell
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Editors and Affiliations

  1. University of Rome Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    Alberto Pettorossi

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Caldwell, J.L. (2002). Extracting General Recursive Program Schemes in Nuprl’s Type Theory. In: Pettorossi, A. (eds) Logic Based Program Synthesis and Transformation. LOPSTR 2001. Lecture Notes in Computer Science, vol 2372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45607-4_13

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  • DOI: https://doi.org/10.1007/3-540-45607-4_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43915-8

  • Online ISBN: 978-3-540-45607-0

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