Typed normal form bisimulation

  • Authors:
  • Soren B. Lassen;Paul Blain Levy

  • Affiliations:
  • Google, Inc.;University of Birmingham, UK

  • Venue:
  • CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
  • Year:
  • 2007

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Abstract

Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize Lévy-Longo tree equivalence and Boehm tree equivalence. It has been adapted to a range of un-typed, higher-order calculi, but types have presented a difficulty. In this paper, we present an account of normal form bisimulation for types, including recursive types. We develop our theory for a continuation-passing style calculus, Jump-With-Argument (JWA), where normal form bisimilarity takes a very simple form. We give a novel congruence proof, based on insights from game semantics. A notable feature is the seamless treatment of eta-expansion. We demonstrate the normal form bisimulation proof principle by using it to establish a syntactic minimal invariance result and the uniqueness of the fixed point operator at each type.