Chapter 1 CIRC

CIRC is an automated circular coinductive prover that is implemented as an extension of Maude. CIRC implements the circularity principle, which generalizes circular coinductive deduction [4] and can be expressed in plain English as follows. Assume that each equation of interest (to be proved) e admits a frozen form fr(e) and a set of derived equations, its derivatives, Der(e). The circularity principle requires that the following rule be valid: if from the hypothesis H together with fr (e) we can deduce Der (e), then e is a consequence of H. When fr (e) freezes the equation at the top as in [4], the circularity principle becomes circular coinduction. Interestingly, when the equation is frozen at the bottom on a variable, then it becomes a structural induction (on that variable) derivation rule. This way, CIRC supports both coinduction and induction as projections of a more general principle. In this paper, we concentrate on CIRC's coinductive capabilities. Acknowledgment. We are grateful to Andrei Popescu for his essential contribution at the implementation of the first version of the tool. The current version of CIRC includes many of his brilliant ideas.