Proving properties about functions on lists involving element tests

  • Authors:
  • Daniel Seidel;Janis Voigtländer

  • Affiliations:
  • Rheinische Friedrich-Wilhelms, Universität Bonn Institut für Informatik, Bonn, Germany;Rheinische Friedrich-Wilhelms, Universität Bonn Institut für Informatik, Bonn, Germany

  • Venue:
  • WADT'10 Proceedings of the 20th international conference on Recent Trends in Algebraic Development Techniques
  • Year:
  • 2010

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Abstract

Bundy and Richardson [4] developed a method for reasoning about functions manipulating lists which is based on separating shape from content, and then exploiting a mathematically convenient representation for expressing shape-only manipulations. Later, Prince et al. [7] extended the technique to other data structures, and gave it a more formal basis via the theory of containers. All these results are restricted to fully polymorphic functions. For example, functions using equality tests on list elements are out of reach. We remedy this situation by developing new abstractions and representations for less polymorphic functions. In Haskell speak, we extend the earlier approach to be applicable in the presence of (certain) type class constraints.