Proving Existential Theorems when Importing Results from MDG to HOL

An existential theorem, for the specification or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verification result from one verification system to another system. In this paper, we investigate the verification of the existential theorems of hardware specifications and implementations. Whilst much of the approach is generally applicable, we specifically consider a hybrid system linking the MDG hardware verification system with the HOL interactive proof system. We investigate existential theorems based on the syntax and semantics of the MDG input language (MDG-HDL) in HOL. We define an output representation for each component in the MDG-HDL component library. We summarize a general method which is used to prove the existential theorem for any MDG-HDL program. The method can also be used to solve other existentially quantified goals.