Using Theory Morphisms for Implementing Formal Methods Tools

Tools for a specification language can be implemented directly (by building a special purpose theorem prover) or by a conservative embedding into a typed meta-logic, which allows their safe and logically consistent implementation and the reuse of existing theorem prover engines. For being useful, the conservative extension approach must provide derivations for several thousand “folklore” theorems. In this paper, we present an approach for deriving the mass of these theorems mechanically from an existing library of the meta-logic. The approach presupposes a structured theory morphism mapping library datatypes and library functions to new functions of the specification language while uniformly modifying some semantic properties; for example, new functions may have a different treatment of undefinedness compared to old ones.