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Basic Operational Preorders for Algebraic Effects in General, and for Combined Probability and Nondeterminism in Particular

Authors Aliaume Lopez, Alex Simpson

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Aliaume Lopez
  • École Normale Supérieure Paris-Saclay, Université Paris-Saclay, France
Alex Simpson
  • Faculty of Mathematics and Physics, University of Ljubljana, Slovenia

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Aliaume Lopez and Alex Simpson. Basic Operational Preorders for Algebraic Effects in General, and for Combined Probability and Nondeterminism in Particular. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CSL.2018.29

Abstract

The "generic operational metatheory" of Johann, Simpson and Voigtländer (LiCS 2010) defines contextual equivalence, in the presence of algebraic effects, in terms of a basic operational preorder on ground-type effect trees. We propose three general approaches to specifying such preorders: (i) operational (ii) denotational, and (iii) axiomatic; coinciding with the three major styles of program semantics. We illustrate these via a nontrivial case study: the combination of probabilistic choice with nondeterminism, for which we show that natural instantiations of the three specification methods (operational in terms of Markov decision processes, denotational using a powerdomain, and axiomatic) all determine the same canonical preorder. We do this in the case of both angelic and demonic nondeterminism.

Subject Classification

ACM Subject Classification
  • Theory of computation → Operational semantics
  • Theory of computation → Denotational semantics
  • Theory of computation → Axiomatic semantics
Keywords
  • contextual equivalence
  • algebraic effects
  • operational semantics
  • domain theory
  • nondeterminism
  • probabilistic choice
  • Markov decision process

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