Sufficient Completeness and Parameterized Proofs by Induction

Theorem proving in parameterized specifications allows for shorter and more structured proofs. Moreover, a generic proof can be given just once and reused for each instantiation of the parameters. We present procedures to test sufficient completeness and to prove and disprove inductive properties automatically in parameterized conditional specifications. This new method when limited to non-parameterized conditional specifications, can refute general clauses; refutational completeness is also preserved for boolean ground convergent rewrite systems even if the functions are not sufficiently complete and the constructors are not free. The method has been implemented in the prover SPIKE. Based on computer experiments, the method appears to be more practical and efficient than inductive theorem proving in non-parameterized specifications. Moreover, SPIKE offers facilities to check and complete definitions.

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