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A Contextual Reconstruction of Monadic Reflection

Authors: Toru Kawata

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

With the help of an idea of contextual modal logic, we define a logical system lambda^{refl} that incorporates monadic reflection, and then investigate delimited continuations through the lens of monadic reflection. Technically, we firstly prove a certain universality of continuation monad, making the character of monadic reflection a little more clear. Next, moving focus to delimited continuations, we present a macro definition of shift/reset by monadic reflection. We then prove that lambda^{refl}_{2cont}, a restriction of lambda^{refl}, has exactly the same provability as lambda^{s/r}_{pure}, a system that incorporates shift/reset. Our reconstruction of monadic reflection opens up a path for investigation of delimited continuations with familiar monadic language.

Cite as

Toru Kawata. A Contextual Reconstruction of Monadic Reflection. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 27:1-27:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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  author =	{Kawata, Toru},
  title =	{{A Contextual Reconstruction of Monadic Reflection}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.27},
  URN =		{urn:nbn:de:0030-drops-96947},
  doi =		{10.4230/LIPIcs.CSL.2018.27},
  annote =	{Keywords: Monadic Reflection, Delimited Continuations, shift/reset, Contextual Modal Logic, Curry-Howard Isomorphism}
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