We present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program equivalence in calculi with single-prompted delimited control. The basic theory that we develop is presented using Madiot et al.'s framework that allows for smooth integration and composition of up-to techniques facilitating bisimulation proofs. We also generalize the framework in order to express environmental bisimulations that support equivalence proofs of evaluation contexts representing continuations. This change leads to a novel and powerful up-to technique enhancing bisimulation proofs in the presence of control operators.
@InProceedings{aristizabal_et_al:LIPIcs.FSCD.2016.9, author = {Aristiz\'{a}bal, Andr\'{e}s and Biernacki, Dariusz and Lenglet, Sergue\"{i} and Polesiuk, Piotr}, title = {{Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation}}, booktitle = {1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)}, pages = {9:1--9:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-010-1}, ISSN = {1868-8969}, year = {2016}, volume = {52}, editor = {Kesner, Delia and Pientka, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.9}, URN = {urn:nbn:de:0030-drops-59756}, doi = {10.4230/LIPIcs.FSCD.2016.9}, annote = {Keywords: delimited continuation, dynamic prompt generation, contextual equivalence, environmental bisimulation, up-to technique} }
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