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International Conference on Automated Deduction

CADE 1984: 7th International Conference on Automated Deduction pp 209–223Cite as

A Linear Time Algorithm for a Subcase of Second Order Instantiation

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 170))

Abstract

A problem that comes up in any proof-checking system is whether or not a proof step is a valid instantiation of a lemma or theorem. Often, the lemma or theorem may include set variables and so in general can be second order. This problem is somewhat simpler than the more general problem of second order unification. Jensen and Pietrzykowski [1] and Huet [2] give semi-decision procedures for finding ω-order unifiers. The second order instantiantion problem is shown to be NP-complete in Baxter [3]. Our approach will be to find useful subcases of the second order instantiantion problem which yield to fast algorithms. This paper is a first approximation towards that goal.

This work was supported in part by National Science Foundation Grants MCS-8011417 and MCS-831499

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References

  1. T. Pietrzykowski, “A Complete Mechanization of Second Order Type Theory”, (1973), JACM 20, 333–364.

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  2. D. C. Jensen and T. Pietrzykowski, “Mechanizing ω-Order Type Theory Through Unification”, (1976) Theorectical Computer Science 3, 123–171.

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  3. G. Hunt, “A Mechanization of Type Theory”, (1975), Theorectical Computer Science 1, 25–58.

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  4. L. D. Baxter, “The Complexity of Unification,” (1976), Doctoral Thesis, Dept. of Computer Science, University of Waterloo, Waterloo, Ontario.

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Author information

Authors and Affiliations

  1. University of Texas at Austin, Texas

    Donald Simon

Authors
  1. Donald Simon
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Editor information

Editors and Affiliations

  1. SRI International, 333 Ravenswood Avenue, Menlo Park, CA, 94025, USA

    R. E. Shostak

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© 1984 Springer-Verlag Berlin Heidelberg

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Simon, D. (1984). A Linear Time Algorithm for a Subcase of Second Order Instantiation. In: Shostak, R.E. (eds) 7th International Conference on Automated Deduction. CADE 1984. Lecture Notes in Computer Science, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34768-4_13

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  • DOI: https://doi.org/10.1007/978-0-387-34768-4_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96022-7

  • Online ISBN: 978-0-387-34768-4

  • eBook Packages: Springer Book Archive

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