Formally Linking MDG and HOL Based on a Verified MDG System

We describe an approach for formally linking a symbolic state enumeration system and a theorem proving system based on a verified version of the former. It has been realized using a simplified version of the MDG system and the HOL system. Firstly, we have verified aspects of correctness of a simplified version of the MDG system. We have made certain that the semantics of a program is preserved in those of its translated form. Secondly, we have provided a formal linkage between the MDG system and the HOL system based on importing theorems. The MDG verification results can be formally imported into HOL to form a HOL theorem. Thirdly, we have combined the translator correctness theorems and importing theorems. This allows the MDG verification results to be imported in terms of a high level language (MDG-HDL) rather than a low level language. We also summarize a general method to prove existential theorems for the design. The feasibility of this approach is demonstrated in a case study that integrates two applications: hardware verification (in MDG) and usability verification (in HOL). A single HOL theorem is proved that integrates the two results.

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