We present direct equational axiomatizations of the call-by-value lambda calculus with the control operators shift_0 and reset_0 that generalize Danvy and Filinski's shift and reset in that they allow for abstracting control beyond the top-most delimited continuation. We address an untyped version of the calculus as well as a typed version with effect subtyping. For each of the calculi we present a set of axioms that we prove sound and complete with respect to the corresponding CPS translation.
@InProceedings{materzok:LIPIcs.CSL.2013.521, author = {Materzok, Marek}, title = {{Axiomatizing Subtyped Delimited Continuations}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {521--539}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.521}, URN = {urn:nbn:de:0030-drops-42178}, doi = {10.4230/LIPIcs.CSL.2013.521}, annote = {Keywords: Delimited Continuations, Continuation Passing Style, Axiomatization} }
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