A mathematical model of inheritance

摘要

Inheritance is regarded as the hallmark of object-oriented programming languages. A mathematical model of inheritance is presented. In this model, the graph-sorted signature is introduced to represent the algebraic structure of the program, and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance. The program's algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language's inheritance.