Verifiable and executable theories of design for synthesizing correct hardware

Formally verified hardware synthesis functions have been developed and implemented using high-order logic, automatic theorem provers, and declarative languages. The synthesis functions, which take the form of equivalence-preserving transformations, enable implementations to be related to their specifications in a formally verified manner. As shown by the theory of design for array multipliers, verified synthesis functions produce implementations which are correct by construction, thus avoiding the exponential growth in effort inherent in simulation-based and Boolean comparison-based verification. Theories of design with their verified synthesis functions and correctness theorems represent additional features which would logically extend computer-aided design systems for design synthesis and design verification