Descriptive and relative completeness of logics for higher-order functions

  • Authors:
  • Kohei Honda;Martin Berger;Nobuko Yoshida

  • Affiliations:
  • Department of Computer Science, Queen Mary, University of London;Department of Computer Science, Queen Mary, University of London;Department of Computing, Imperial College London

  • Venue:
  • ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
  • Year:
  • 2006

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Abstract

This paper establishes a strong completeness property of compositional program logics for pure and imperative higher-order functions introduced in [18, 16, 17, 19, 3]. This property, called descriptive completeness, says that for each program there is an assertion fully describing the program's behaviour up to the standard observational semantics. This formula is inductively calculable from the program text alone. As a consequence we obtain the first relative completeness result for compositional logics of pure and imperative call-by-value higher-order functions in the full type hierarchy