LIPIcs.CALCO.2015.116.pdf
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A Recipe for State-and-Effect Triangles
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Volume:
6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Algebra and Coalgebra in Computer Science (CALCO) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2015-10-28
Cite As Get BibTex
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.
Subject Classification
Keywords
- Duality
- predicate transformer
- state transformer
- state-and-effect triangle
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