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A Design Structure for Higher Order Quotients

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Theorem Proving in Higher Order Logics (TPHOLs 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3603))

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Abstract

The quotient operation is a standard feature of set theory, where a set is partitioned into subsets by an equivalence relation. We reinterpret this idea for higher order logic, where types are divided by an equivalence relation to create new types, called quotient types. We present a design to mechanically construct quotient types as new types in the logic, and to support the automatic lifting of constants and theorems about the original types to corresponding constants and theorems about the quotient types. This design exceeds the functionality of Harrison’s package, creating quotients of multiple mutually recursive types simultaneously, and supporting the equivalence of aggregate types, such as lists and pairs. Most importantly, this design supports the creation of higher order quotients, which enable the automatic lifting of theorems with quantification over functions of any higher order.

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Author information

Authors and Affiliations

  1. U.S. Department of Defense,  

    Peter V. Homeier

Authors
  1. Peter V. Homeier
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Editor information

Editors and Affiliations

  1. Computing Laboratory, Oxford University,  

    Joe Hurd

  2. Computing Laboratory, Oxford University, Wolfson Building, Parks Road Oxford, OX1 3QD, UK

    Tom Melham

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© 2005 Springer-Verlag Berlin Heidelberg

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Homeier, P.V. (2005). A Design Structure for Higher Order Quotients. In: Hurd, J., Melham, T. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2005. Lecture Notes in Computer Science, vol 3603. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11541868_9

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  • DOI: https://doi.org/10.1007/11541868_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28372-0

  • Online ISBN: 978-3-540-31820-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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