General Framework for Mechanizing Induction using Test Set

We present in this paper a test set induction procedure which is refutationally complete for conditional specifications (not restricted to Boolean specifications), in that it refutes any conjecture which is not an inductive theorem. Previously, we could only compute a test set for a conditional specification if the constructors were free. Here, we give a new definition of test sets and a procedure to compute them even if the constructors are not free. The method uses a new notion of provable inconsistency and induction positions (that need to be instantiated by induction schemes) which allows us to refute more false conjectures than with previous approaches. We also present an algorithm to compute all the induction positions of a conditional specification. The method has been implemented in SPIKE. Computer experiments show the superiority of SPIKE concerning mutual induction over explicit induction based systems.