中文摘要：

为探讨包含构造操作和观察操作的范畴数据类型上的子类型关系及性质,将双代数作为范畴数据类型上构造操作和观察操作的统一数学描述,分析了归纳数据类型上代数子类型和共归纳数据类型上共代数子类型的范畴论定义及其语义,给出了双代数结构中代数子类型和共代数子类型的范畴论定义及其语义解释,从而将代数子类型和共代数子类型的研究扩展到双代数上.

英文摘要：

Abstract：In order to investigate the subtype relationships and the properties of categorical data types which usually contain both construction operations and observation operations,this paper adopts the bialgebras to bring about a unified mathematical description of the construction operations and observations operations of categorical data types,and analyzes categorical definitions and their semantics,which are both used to describe the algebraic subtypes of inductive data types and the coalgebraic subtypes of coinductive data types,as well as the algebraic and coalgebraic subtypes in bialgebraic structures.Thus,the researches on the algebraic and coalgebraic subtypes are extended to the bialgebras.