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A Recipe for State-and-Effect Triangles

Author Bart Jacobs



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LIPIcs.CALCO.2015.116.pdf
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Bart Jacobs

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Bart Jacobs. A Recipe for State-and-Effect Triangles. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 116-129, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CALCO.2015.116

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.
Keywords
  • Duality
  • predicate transformer
  • state transformer
  • state-and-effect triangle

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