A Resolution for Scalability Problem of Record Datatype Based Formal Memory Models in Coq

The formal memory model is one of the most critical components for program verification tools development. Theoretically, the record datatype based formal memory model is a type of intuitive and efficient formalization scheme. However, practical applications of record datatype based formal memory models in Coq are limited because of their scalability problem. Present work addresses this issue by defining a new multi-level table framework with modular polymorphism in Coq. First, we present polymorphic meta specifications of formal memory model and corresponding operations. Second, through the combination of polymorphic instantiation and recursive nesting of modules, we simulate the linear and tail recursion principles. With these principles, a new record type based abstract specifications of formal memory model with multi-level table structure and corresponding memory operations are constructed. Finally, we define a logic-physical memory conversion ratio to quantify the optimization of scalability, and we present a series experiments based on the ratio to certify the improvement of scalability of the optimized framework in Coq compared with conventional definitions.