Turi and Plotkin introduced an elegant approach to structural operational semantics based on universal coalgebra, parametric in the type of syntax and the type of behaviour. Their framework includes abstract GSOS, a categorical generalisation of the classical GSOS rule format, as well as its categorical dual, coGSOS. Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence. Unfortunately, the combination of the two formats does not feature these desirable properties. We show that monotone specifications—that disallow negative premises—do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.

中文翻译：

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单调规范的分配法则

Turi和Plotkin提出了一种基于通用结余，语法类型和行为类型参数化的结构化操作语义的优雅方法。他们的框架包括抽象GSOS，经典GSOS规则格式的分类概括，以及其分类对偶coGSOS。在每种规范都有一个唯一的模型上，行为对等是一致的，从某种意义上说，两种格式都表现良好。不幸的是，两种格式的组合没有这些理想的特性。我们表明，单调规范-不允许否定前提-确实会引起单子在共纳体上的规范分布定律，因此产生了独特的成分解释。