Chu Spaces and Their Interpretation as Concurrent Objects
Chu Spaces and Their Interpretation as Concurrent Objects
复制标题
DOI：
10.1007/bfb0015256
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
V. Pratt
中科院分区：
文献类型：
--
作者：
V. Pratt
阿楚空间是一个二元关系 从一个集合A到一个反集合X，定义为一个集合，通过匡威函数进行变换。Chu空间允许许多解释，因为它实现了所有小的具体范畴，以及数学和计算实践中出现的大多数大范畴。计算机科学特别感兴趣的是它们作为计算过程的解释，其中A是在时间上分布的事件的时间表，X是在Scott意义上形成信息系统的状态的自动机，并且在 关系是历史形成的个人的转变。将传统的X上转移和A上优先的齐次二元关系分别恢复为异构二元关系的左、右残差 与自己。Chu空间的自然代数是线性逻辑的自然代数，通过过程解释使之成为过程代数。
A Chu space is a binary relation from a setAto an antisetXdefined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takesAto be a schedule of events distributed in time,Xto be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition onXand precedence onAare recovered as respectively the right and left residuals of the heterogeneous binary relation with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.