Semantic Behavior of Indexed Co-inductive Data Type in Fibrational Setting

Miao De-cheng, Xi Jian-qing, Jiang Chang-jin, Liang Yong-lin
2016 International Journal of u- and e- Service, Science and Technology  
Traditional methods such as category theory and coalgebra have some drawbacks to analyze semantic behavior of indexed co-inductive data type. Aiming at the problem above, this paper explored indexed co-inductive data type in programming by Fibrations theory. Our main work was that we firstly made some basic logical structures of indexed co-inductive data type over a fibration such as truth and quotient functor; using endo-functor in base categories and their equation-preserving lifting in total
more » ... categories, then we analyzed semantic behavior of indexed co-inductive data type; at last we briefly introduced applications of Fibrations theory on indexed co-inductive data type by example. Compared with traditional methods, brief descriptions and flexible expansibility of Fibrations theory can analyze semantic behavior of indexed co-inductive data type accurately, and superior abstractness of Fibrations theory doesn't rely on particular computing environments to compute semantics. 254 Copyright ⓒ 2016 SERSC constructing functor lifted in total category to depict abstractly semantic computing and program logics of indexed co-inductive data type, Hermida and Jacobs did lots of works in this field [9] . In this paper, we applying Fibrations theory to research indexed co-inductive data type, by taking indexed co-inductive data type to be object set in base category, taking their semantic behavior to be object set in total category firstly; then we establish the responsible relation in program logic directly between indexed co-inductive data type and it semantic behavior by equation functor and quotient functor. Our primary works are studying semantic behavior of indexed co-inductive data type and its co-inductive rule by Fibrations theory. The rest of this paper is structured as follows. In Section 2,we firstly introduced some basic concepts needed for our works, such as Cartesian arrow and fibration. In Section 3, we presented indexed fibration et al. based on slice category to analyze semantic behavior of indexed co-inductive data type, and introduced the applications of Fibrations theory briefly by example. Then we researched some related works in the field of co-inductive data type currently in Section 4. At last, we summarized our conclusions and discussed our future works.
doi:10.14257/ijunesst.2016.9.6.24 fatcat:5m5527cewjg7ddewhs3qmk6ctu