  In this paper, we introduce open parity games, which is a compositional
approach to parity games. This is achieved by adding open ends to the usual
notion of parity games. We introduce the category of open parity games, which
is defined using standard definitions for graph games. We also define a
graphical language for open parity games as a prop, which have recently been
used in many applications as graphical languages. We introduce a suitable
semantic category inspired by the work by Grellois and Melli\`es on the
semantics of higher-order model checking. Computing the set of winning
positions in open parity games yields a functor to the semantic category.
Finally, by interpreting the graphical language in the semantic category, we
show that this computation can be carried out compositionally.
