Logical Methods in Computer Science (Nov 2007)

Generic Trace Semantics via Coinduction

  • Ichiro Hasuo,
  • Bart Jacobs,
  • Ana Sokolova

DOI
https://doi.org/10.2168/LMCS-3(4:11)2007
Journal volume & issue
Vol. Volume 3, Issue 4

Abstract

Read online

Trace semantics has been defined for various kinds of state-based systems, notably with different forms of branching such as non-determinism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these "trace semantics," namely coinduction in a Kleisli category. This claim is based on our technical result that, under a suitably order-enriched setting, a final coalgebra in a Kleisli category is given by an initial algebra in the category Sets. Formerly the theory of coalgebras has been employed mostly in Sets where coinduction yields a finer process semantics of bisimilarity. Therefore this paper extends the application field of coalgebras, providing a new instance of the principle "process semantics via coinduction."

Keywords