Abstract:

There are some drawbacks for traditional modeling methods of data model of sharing system in analyzing semantic properties and describing semantic behaviors. Aiming at the problems mentioned above we present a data model of sharing system based on Fibrations theory. We contribute in the following two aspects. Firstly, we accurately analyze semantic properties by combining algebras methods with truth functor, lifting preserving-truth and comprehension functor, and formally depict semantic behaviors by combining co-algebras methods with equation functor, lifting preserving-equation and quotient functor. Secondly, in the framework of Fibrations theory we construct parameterized recursive and co-recursive operations on complex inductive and co-inductive data structure to abstractly describe inductive and co-inductive rules with universality, and briefly introduce applications of Fibrations theory by examples. Compared with traditional methods such as category theory, the Fibrations theory of brief descriptions and flexible expansibility can accurately analyze semantics properties, formally describe semantic behaviors of data model of sharing system, and abstractly depict inductive and co-inductive rules with universality of complex data structures.

Key words: