Hierarchical Reflection

  • Luís Cruz-Filipe
  • Freek Wiedijk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3223)


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.


Normal Form Normalization Function Algebraic Structure Type Theory Function Symbol 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Luís Cruz-Filipe
    • 1
    • 2
  • Freek Wiedijk
    • 1
  1. 1.NIIIRadboud University of Nijmegen 
  2. 2.Center for Logic and ComputationLisboa

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