计算机科学中的共代数方法的研究综述

代数理论已经在抽象数据类型、程序语义等计算机科学领域有了广泛的应用,而代数的对偶概念--共代数,则直到20世纪90年代中后期才被越来越多的计算机学者关注.代数从"构造"的角度研究数据类型,而共代数则从"观察"的角度考察系统及其性质.共代数方法对研究基于状态的系统有独特的优越性,可以对系统的行为等价、不确定性等从数学上进行深入的探讨.目前,共代数理论已经逐步应用在自动机理论、并发程序的语义、面向对象程序的规范等领域.对共代数的基本概念、范畴理论基础、共代数逻辑及应用等方面的最新研究成果进行了介绍,以引起国内相关研究领域的学者对计算机科学中的共代数方法的关注.

A Survey on the Coalgebraic Methods in Computer Science

Unlike the widespread applications of algebraic methods in computer science, coalgebraic methods, as the dual concepts of algebras, have not been noticed by computer scientists till the mid 1990s. In algebraic methods, the constructive elements of data types are studied, while in coalgebraic methods, the observable behaviors of systems are investigated. Coalgebraic methods have distinct advantages in mathematic study of state-based systems since them enable the depth research on those systems?properties such as behavior equivalence, nondeterminism and so on. Coalgebraic methods have also been applied in many research fields, for example, automata theory, semantics of concurrency, specifications of object-oriented software etc. The recent progress of coalgebraic methods, including its basic concepts, categorical foundations, logical foundations and its applications, is summarized for raising the attention of the relative researchers.