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TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
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TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
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Buhler et al. presented a mathematical theory of toss juggling by regarding a toss pattern as an arithmetic function, where the function must satisfy a condition for the pattern to be valid. In this paper, the theory is formalized in terms of coinduction, reflecting the fact that the validity of toss juggling is related to a property of infinite phenomena. A tactic is implemented for proving the validity of toss patterns in Coq. Additionally, the completeness and soundness of a well-known algorithm for checking the validity is demonstrated. The result exposes a practical aspect of coinductive proofs.