{"title":"Environmental Bisimulations for Higher-Order Languages","authors":"D. Sangiorgi, N. Kobayashi, Eijiro Sumii","doi":"10.1145/1889997.1890002","DOIUrl":null,"url":null,"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.","PeriodicalId":137827,"journal":{"name":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"164","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1889997.1890002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 164
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.