相互作用与观察：反应系统通过对偶代数的范畴语义
Interaction and observation: categorical semantics of reactive systems trough dialgebras
摘要：
我们使用双代数，广义代数和coalgebras，作为补充的标准coalgebra框架，旨在描述的语义的交互系统的反应规则的手段。在这个模型中，交互是内置的，语义等价性由此产生，而不是由孤立的组件的副作用（可能很难）的理解来确定。双代数中的行为等价由给定过程如何与其他过程相互作用以及所获得的观察结果确定。我们开发了一种技术来定义不同函子的双代数的类别，特别是允许我们比较标准的共代数语义和它的双代数对应。我们使用CCS和π演算的框架。值得注意的是，给予π演算语义的双代数不需要使用预层范畴。
英文摘要：
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the pi-calculus does not require the use of presheaf categories.
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