γ演算到Action演算的转换

Translating γ-Calculus into Action Calculus

Action演算簇(action calculi)作为描述不同并发交互行为的数学框架,可以表示一大类具有某些相同特性的并发形式化模型.试图把g演算(一种基于约束的高阶并发计算模)也包含在action演算簇的框架下.首先定义了一个具体的action演算AC(Kg),然后给出了从g演算到AC(Kg)转换的形式描述,最后在定义AC(Kg)的可观察性、弱互模拟关系和弱等价关系的基础上,以p演算为中间表示,证明了这种转换保持了g演算的弱行为等价性.研究表明,action演算簇可以表示基于约束的并发模型,从而充分说明了action演算簇的描述能力,并且为在action演算簇框架下把g演算与其他并发模型结合并进行比较提供了前提.

Action calculi is introduced as a mathematical framework for expressing different interactive behaviors, which shows the advantages in representing different interactive models with some common features. In this paper, action calculi is used to include g-calculus (a computational calculus for higher-order concurrent programming) in its setting. First, a concrete action calculus AC(Kg) is defined. Then the formal compositional translation of the g-calculus into AC(Kg) is presented. Finally, upon definitions of the observability, the weak barbed bisimularity as well as the weak barbed congruence for AC(Kg), it is proved that such translation preserves the weak behavioural equivalence of the g-calculus with the p-calculus as intermediate. This work not only shows the expressiveness of action calculi, but also provides precondition for uniting and comparing g-calculus with other concurrent models under the theory of action calculi.