  Compositionality proofs in higher-order languages are notoriously involved,
and general semantic frameworks guaranteeing compositionality are hard to come
by. In particular, Turi and Plotkin's bialgebraic abstract GSOS framework,
which has been successfully applied to obtain off-the-shelf compositionality
results for first-order languages, so far does not apply to higher-order
languages. In the present work, we develop a theory of abstract GSOS
specifications for higher-order languages, in effect transferring the core
principles of Turi and Plotkin's framework to a higher-order setting. In our
theory, the operational semantics of higher-order languages is represented by
certain dinatural transformations that we term pointed higher-order GSOS laws.
We give a general compositionality result that applies to all systems specified
in this way and discuss how compositionality of the SKI calculus and the
$\lambda$-calculus w.r.t. a strong variant of Abramsky's applicative
bisimilarity are obtained as instances.
