License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2019.18
URN: urn:nbn:de:0030-drops-105256
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10525/
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Espírito Santo, José ; Pinto, Luís ; Uustalu, Tarmo

Modal Embeddings and Calling Paradigms

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LIPIcs-FSCD-2019-18.pdf (0.5 MB)

Abstract

We study the computational interpretation of the two standard modal embeddings, usually named after Girard and Gödel, of intuitionistic logic into IS4. As source system we take either the call-by-name (cbn) or the call-by-value (cbv) lambda-calculus with simple types. The target system can be taken to be the, arguably, simplest fragment of IS4, here recast as a very simple lambda-calculus equipped with an indeterminate lax monoidal comonad. A slight refinement of the target and of the embeddings shows that: the target is a calculus indifferent to the calling paradigms cbn/cbv, obeying a new paradigm that we baptize call-by-box (cbb), and enjoying standardization; and that Girard's (resp. Gödel's) embbedding is a translation of cbn (resp. cbv) lambda-calculus into this calculus, using a compilation technique we call protecting-by-a-box, enjoying the preservation and reflection properties known for cps translations - but in a stronger form that allows the extraction of standardization for cbn or cbv as consequence of standardization for cbb. The modal target and embeddings achieve thus an unification of call-by-name and call-by-value as call-by-box.

BibTeX - Entry

@InProceedings{espritosanto_et_al:LIPIcs:2019:10525,
  author =	{Jos{\'e} Esp{\'i}rito Santo and Lu{\'i}s Pinto and Tarmo Uustalu},
  title =	{{Modal Embeddings and Calling Paradigms}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Herman Geuvers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10525},
  URN =		{urn:nbn:de:0030-drops-105256},
  doi =		{10.4230/LIPIcs.FSCD.2019.18},
  annote =	{Keywords: intuitionistic S4, call-by-name, call-by-value, comonadic lambda-calculus, standardization, indifference property}
}

Keywords: intuitionistic S4, call-by-name, call-by-value, comonadic lambda-calculus, standardization, indifference property
Collection: 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)
Issue Date: 2019
Date of publication: 18.06.2019

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