Abstract 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 i