Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Using A Generalisation Critic to Find Bisimulations for Coinductive Proofs
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
A coalgebraic approach to the semantics of the ambient calculus
Theoretical Computer Science - Algebra and coalgebra in computer science
Regular Strategies as Proof Tactics for CIRC
Electronic Notes in Theoretical Computer Science (ENTCS)
Circular Coinduction with Special Contexts
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
CIRC: a circular coinductive prover
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Circular coinduction: a proof theoretical foundation
CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Incremental pattern-based coinduction for process algebra and its isabelle formalization
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
The power of parameterization in coinductive proof
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Coalgebra has in recent years been recognized as the framework of choice for the treatment of reactive systems at an appropriate level of generality. Proofs about the reactive behavior of a coalgebraic system typically rely on the method of coinduction. In comparison to ‘traditional' coinduction, which has the disadvantage of requiring the invention of a bisimulation relation, the method of circular coinduction allows a higher degree of automation. As part of an effort to provide proof support for the algebraic-coalgebraic specification language CoCasl, we develop a new coinductive proof strategy which iteratively constructs a bisimulation relation, thus arriving at a new variant of circular coinduction. Based on this result, we design and implement tactics for the theorem prover Isabelle which allow for both automatic and semiautomatic coinductive proofs. The flexibility of this approach is demonstrated by means of examples of (semi-)automatic proofs of consequences of CoCasl specifications, automatically translated into Isabelle theories by means of the Bremen heterogeneous Casl tool set Hets.