Case Studies in Meta-Level Theorem Proving

We describe an extension of the Pvs system that provides a reasonably eecient and practical notion of reeection and thus allows for soundly adding formalized and veriied new proof procedures. These proof procedures work on representations of a part of the underlying logic and their correctness is expressed at the object level using a computational reeection function. The implementation of the Pvs system has been extended with an eecient evaluation mechanism, since the prac-ticality of the approach heavily depends on careful engineering of the core system, including eecient normalization of functional expressions. We exemplify the process of applying meta-level proof procedures with a detailed description of the encoding of cancellation in commutative monoids and of the kernel of a BDD package.