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 provides 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 \emph{(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 combinatory logics and the $λ$-calculus w.r.t.\ a strong variant of Abramsky's applicative bisimilarity are obtained as instances.

翻译：高阶语言的组合性证明以复杂著称，而能保证组合性的通用语义框架也难以获得。具体而言，Turi与Plotkin的双代数抽象GSOS框架为一阶语言提供了现成的组合性结果，但目前尚不适用于高阶语言。在本文中，我们发展了一套面向高阶语言的抽象GSOS规范理论，实质上将Turi与Plotkin框架的核心原则迁移至高阶设定。在我们的理论中，高阶语言的操作语义由某种称为"（带点的）高阶GSOS律"的二元自然变换表示。我们给出了适用于所有以此方式规范系统的通用组合性结果，并讨论了组合逻辑与λ-演算关于Abramsky的强应用双模拟变体的组合性如何作为特例导出。