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International Conference on Theorem Proving in Higher Order Logics

TPHOLs 1996: Theorem Proving in Higher Order Logics pp 191–201Cite as

Set theory, higher order logic or both?

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1125))

Abstract

The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, but not higher order logic. This paper discusses some approaches to getting the best of both worlds: the expressiveness and standardness of set theory with the efficient treatment of functions provided by typed higher order logic.

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Authors and Affiliations

  1. University of Cambridge Computer Laboratory, New Museums Site Pembroke Street, CB2 3QG, Cambridge, U.K.

    Mike Gordon

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  1. Mike Gordon
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Editor information

Gerhard Goos Juris Hartmanis Jan van Leeuwen Joakim von Wright Jim Grundy John Harrison

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© 1996 Springer-Verlag Berlin Heidelberg

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Gordon, M. (1996). Set theory, higher order logic or both?. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105405

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  • DOI: https://doi.org/10.1007/BFb0105405

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61587-3

  • Online ISBN: 978-3-540-70641-0

  • eBook Packages: Springer Book Archive

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