Higher-order abstract GSOS is a recent extension of Turi and Plotkin's framework of Mathematical Operational Semantics to higher-order languages. The fundamental well-behavedness property of all specifications within the framework is that coalgebraic strong (bi)similarity on their operational model is a congruence. In the present work, we establish a corresponding congruence theorem for weak similarity, which is shown to instantiate to well-known concepts such as Abramsky's applicative similarity for the lambda-calculus. On the way, we develop several techniques of independent interest at the level of abstract categories, including relation liftings of mixed-variance bifunctors and higher-order GSOS laws, as well as Howe's method.

翻译：高阶抽象GSOS是Turi与Plotkin提出的数学操作语义学框架向高阶语言的最新扩展。该框架内所有规约的基本良构性质在于：其操作模型上的余代数强（双）相似性构成一个同余关系。本研究建立了弱相似性的相应同余定理，并证明该定理可具体化为λ-演算中Abramsky应用相似性等经典概念。在此过程中，我们开发了几种具有独立研究价值的抽象范畴层面技术，包括混合变差双函子的关系提升、高阶GSOS律以及Howe方法。