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arXiv · 1804.08373

Bisimulations for Delimited-Control Operators

Dariusz Biernacki·Sergueï Lenglet·Piotr Polesiuk
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Abstract

We present a comprehensive study of the behavioral theory of an untyped $λ$-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.

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Dariusz Biernacki, Sergueï Lenglet, Piotr Polesiuk. 2019-05-23. Bisimulations for Delimited-Control Operators. https://doi.org/10.23638/lmcs-15(2%3A18)2019

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