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Bisimulations for Delimited-Control Operators
We present a comprehensive study of the behavioral theory of an untyped
-calculus extended with the delimited-control operators shift and
reset. To that end, we define a contextual equivalence for this calculus, that
we then aim to characterize with coinductively defined relations, called
bisimilarities. We consider different styles of bisimilarities (namely
applicative, normal-form, and environmental) within a unifying framework, 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