Automating Coinduction with Case Analysis
Coinduction is a major technique employed to prove behavioral properties of systems, such as behavioral equivalence. Its automation is highly desirable, despite the fact that most behavioral problems are \(\Pi_2^0\)-complete. Circular coinduction, which is at the core of the CIRC prover, automates coinduction by systematically deriving new goals and proving existing ones until, hopefully, all goals are proved. Motivated by practical examples, circular coinduction and CIRC have been recently extended with several features, such as special contexts, generalization and simplification. Unfortunately, none of these extensions eliminates the need for case analysis and, consequently, there are still many natural behavioral properties that CIRC cannot prove automatically. This paper presents an extension of circular coinduction with case analysis constructs and reasoning, as well as its implementation in CIRC. To uniformly prove the soundness of this extension, as well as of past and future extensions of circular coinduction and CIRC, this paper also proposes a general correct-extension technique based on equational interpolants.
KeywordsCase Analysis Special Context Proof System Behavioral Property Reduction Rule
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- 1.Bouhoula, A., Rusinowitch, M.: Automatic case analysis in proof by induction. In: IJCAI, pp. 88–94. Morgan Kaufmann Publishers Inc., San Francisco (1993)Google Scholar
- 6.Goriac, E., Caltais, G., Lucanu, D.: Simplification and Generalization in CIRC. In: 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, IEEE Computer Society, Los Alamitos (2009)Google Scholar
- 9.Niqui, M., Rutten, J.J.M.M.: Sampling, splitting and merging in coinductive stream calculus. In: Mathematics of Program Construction 2010 (MPC 2010) (to appear, 2010); See CWI Technical report SEN-E0904 (2009) http://homepages.cwi.nl/tilde~janr/papers/