Steps and traces

Jurriaan Rot, Bart Jacobs, Paul Levy

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In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg-Moore category. This paper elaborates two new unifying ideas: 1) coalgebraic trace semantics is naturally presented in terms of corecursive algebras, and 2) all three approaches arise as instances of the same abstract setting. Our perspective puts the different approaches under a common roof, and allows to derive conditions
under which some of them coincide.
Original languageEnglish
Pages (from-to)1482–1525
JournalJournal of Logic and Computation
Issue number6
Early online date23 Aug 2021
Publication statusPublished - Sept 2021


  • Coalgebra
  • corecursive algebras
  • trace semantics


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