Bisimulations for Delimited-Control Operators
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We propose a survey of the behavioral theory of an untyped lambda-calculus extended with the delimited-control operators shift and reset. We define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We study different styles of bisimilarities (namely applicative, normal-form, and environmental), and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators.
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