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Hierarchical Reflection

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Theorem Proving in Higher Order Logics (TPHOLs 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3223))

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Abstract

The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even a relation one gets a more general method known as “partial reflection”. In this paper we show how one can take advantage of the partiality of the interpretation to uniformly define a family of tactics for equational reasoning that will work in different algebraic structures. The tactics then follow the hierarchy of those algebraic structures in a natural way.

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Author information

Authors and Affiliations

  1. NIII, Radboud University of Nijmegen,  

    Luís Cruz-Filipe & Freek Wiedijk

  2. Center for Logic and Computation, Lisboa

    Luís Cruz-Filipe

Authors
  1. Luís Cruz-Filipe
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  2. Freek Wiedijk
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Editor information

Editors and Affiliations

  1. School of Computing, University of Utah,  

    Konrad Slind

  2. Electrical and Computer Engineering Department, Utah State University, 4120 Old Main Hill, 84341, Logan, UT, USA

    Annette Bunker

  3. School of Computing, Univ. of Utah, 84112, Salt Lake City, UT, USA

    Ganesh Gopalakrishnan

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© 2004 Springer-Verlag Berlin Heidelberg

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Cruz-Filipe, L., Wiedijk, F. (2004). Hierarchical Reflection. In: Slind, K., Bunker, A., Gopalakrishnan, G. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2004. Lecture Notes in Computer Science, vol 3223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30142-4_5

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  • DOI: https://doi.org/10.1007/978-3-540-30142-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23017-5

  • Online ISBN: 978-3-540-30142-4

  • eBook Packages: Springer Book Archive

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