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Bisimulation proof methods in a path-based specification language for polynomial coalgebras†

Published online by Cambridge University Press:  10 November 2014

XIAO-CONG ZHOU ,
YONG-JI LI ,
WEN-JUN LI ,
HAI-YAN QIAO  and
ZHONG-MEI SHU
XIAO-CONG ZHOU
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510275, P. R. China E-mail: isszxc@mail.sysu.edu.cn
YONG-JI LI
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510275, P. R. China E-mail: isszxc@mail.sysu.edu.cn
WEN-JUN LI
Affiliation:
School of Software, Sun Yat-sen University, Guangzhou 510275, P. R. China
HAI-YAN QIAO
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510275, P. R. China E-mail: isszxc@mail.sysu.edu.cn
ZHONG-MEI SHU
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510275, P. R. China E-mail: isszxc@mail.sysu.edu.cn
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Abstract

What reasoning rules can be used for the deduction of bisimulation formulas in coalgebraic specifications is problematic because those rules used in algebraic specifications possibly cannot be applied to bisimulation formulas. Although some categorical bisimulation proof methods for coalgebras have been proposed, they are not based on specification languages of coalgebras so that they cannot be used as reasoning rules. In this paper, a specification language based on paths of polynomial functors is proposed to specify polynomial coalgebras. Paths of polynomial functors give detailed observations and transitions on the state space of coalgebras so that the techniques used in transition system specifications can be applied to such a path-based language. In particular, because bisimulations can be characterized by paths, the notions of progressions, respectful functions and faithful contexts can be defined based on paths, and then bisimulation up-to proof techniques, including bisimulation up-to bisimilarities and up-to contexts for transition systems can be transformed into reasoning rules in the language. Several examples illustrate how to reason syntactically about bisimulations in the language by using the rules induced by the bisimulation proof techniques.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 4: APLAS 2010 , May 2015 , pp. 765 - 804
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

Supported by the National Natural Science Foundation of China under Grant No. 60673050 and the Fundamental Research Funds for the Central Universities of China under Grant No. 11LGPY39.

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