Kleisli simulation is a categorical notion introduced by Hasuo to verify
finite trace inclusion. They allow us to give definitions of forward and
backward simulation for various types of systems. A generic categorical theory
behind Kleisli simulation has been developed and it guarantees the soundness of
those simulations with respect to finite trace semantics. Moreover, those
simulations can be aided by forward partial execution (FPE)---a categorical
transformation of systems previously introduced by the authors.
In this paper, we give Kleisli simulation a theoretical foundation that
assures its soundness also with respect to infinitary traces. There, following
Jacobs' work, infinitary trace semantics is characterized as the "largest
homomorphism." It turns out that soundness of forward simulations is rather
straightforward; that of backward simulation holds too, although it requires
certain additional conditions and its proof is more involved. We also show that
FPE can be successfully employed in the infinitary trace setting to enhance the
applicability of Kleisli simulations as witnesses of trace inclusion. Our
framework is parameterized in the monad for branching as well as in the functor
for linear-time behaviors; for the former we mainly use the powerset monad (for
nondeterminism), the sub-Giry monad (for probability), and the lift monad (for
exception).Comment: 39 pages, 1 figur
