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URN: urn:nbn:de:0030-drops-55301
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A Recipe for State-and-Effect Triangles

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Abstract

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced 'state-and-effect' triangles which captures this situation categorically, involving an adjunction between state- and predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck's monadicity theorem, to systematically construct such a state-and-effect triangle from an adjunction. The power of this construction is illustrated in many examples, both for the Boolean and probabilistic (quantitative) case.

BibTeX - Entry

@InProceedings{jacobs:LIPIcs:2015:5530,
  author =	{Bart Jacobs},
  title =	{{A Recipe for State-and-Effect Triangles}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{116--129},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Lawrence S. Moss and Pawel Sobocinski},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5530},
  URN =		{urn:nbn:de:0030-drops-55301},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CALCO.2015.116},
  annote =	{Keywords: Duality, predicate transformer, state transformer, state-and-effect triangle}
}

Keywords: Duality, predicate transformer, state transformer, state-and-effect triangle
Seminar: 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
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Issue date: 2015
Date of publication: 2015


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