Environmental Bisimulations for Higher-Order Languages

  • Authors:

  • Davide Sangiorgi;Naoki Kobayashi;Eijiro Sumii

  • Affiliations:

  • University of Bologna, Italy;Tohoku University, Japan;Tohoku University, Japan

  • Venue:
  • LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
  • Year:
  • 2007

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Abstract

Developing a theory of bisimulation in higher-order languages can be hard. Particularly challenging can be: (1) the proof of congruence, as well as enhancements of the bisimulation proof method with "up-to context" techniques, and (2) obtaining definitions and results that scale to languages with different features. To meet these challenges, we present environmental bisimulations, a form of bisimulation for higher-order languages, and its basic theory. We consider four representative calculi: pure \lambda-calculi (call-by-name and call-by-value), call-by-value \lambda-calculus with higher-order store, and then Higher-Order \pi-calculus. In each case: we present the basic properties of environmental bisimilarity, including congruence; we show that it coincides with contextual equivalence; we develop some up-to techniques, including up-to context, as examples of possible enhancements of the associated bisimulation method. Unlike previous approaches (such as applicative bisimulations, logical relations, Sumii-Pierce-Koutavas-Wand), our method does not require induction/indices on evaluation derivation/steps (which may complicate the proofs of congruence, transitivity, and the combination with up-to techniques), or sophisticated methods such as Howe's for proving congruence. It also scales from the pure \lambda-calculi to the richer calculi with simple congruence proofs.