Generic Trace Theory

Trace semantics has been defined for various non-deterministic systems with different input/output types, or with different types of "non-determinism" such as classical non-determinism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms of "trace semantics" are instances of a single categorical construction, namely coinduction in a Kleisli category. This claim is based on our main technical result that an initial algebra in the category of sets and functions yields a final coalgebra in the Kleisli category, for monads with a suitable order structure. The proof relies on coincidence of limits and colimits, like in the work of Smyth and Plotkin. Key words: coalgebra, trace semantics, linear time semantics, monad, Kleisli category, non-determinism, probability

• Type: Journal
• Year: 2006
• Where: ENTCS
• Authors: Ichiro Hasuo, Bart Jacobs, Ana Sokolova
• Keywords: ENTCS 2006, Kleisli Category, Trace Semantics, Various Non-deterministic Systems