Environmental bisimulations for higher-order languages

Davide Sangiorgi, Naoki Kobayashi, Eijiro Sumii

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

65 Citations (Scopus)


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 λ-calculi (call-by-name and call-by-value), call-by-value λ-calculus with higher-order store, and then Higher-Order π-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 bisim-ulations, 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 λ-calculi to the richer calculi with simple congruence proofs.

Original languageEnglish
Title of host publicationProceedings - 22nd Annual IEEE Symposiumon Logic in Computer Science, LICS 2007
Number of pages10
Publication statusPublished - 2007
Event22nd Annual IEEE Symposium on Logic in Computer Science, LICS 2007 - Wroclaw, Poland
Duration: 2007 Jul 102007 Jul 14

Publication series

NameProceedings - Symposium on Logic in Computer Science
ISSN (Print)1043-6871


Conference22nd Annual IEEE Symposium on Logic in Computer Science, LICS 2007


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