Comparing Semantic and Syntactic Methods in Mechanized Proof Frameworks

We present a comparison of semantic and syntactic proof methods for reasoning about typed assembly languages in Coq. We make available our complete Coq developments for a simple and easily understood benchmark system presenting both styles of soundness proof to the same interface. The syntactic proof is standard subject reduction; the semantic proof uses Gödal Löb modal logic, shallowly embedded in Coq. The proof style of the modal logic is flexible and facilitates experimental modifications to the underlying machine. As an example of this flexibility, we discuss how to add fault tolerance to the list machine. In addition, we discus how the the choice of proof methodology affects the trusted computing base of a typed assembly language system.