On the verification of VDM specification and refinement with PVS

Although the formal method VDM has been in existence since the 1970s, there are still no satisfactory tools to support verification in VDM. The paper deals with one possible means of approaching this problem by using the PVS theorem-prover. It describes a translation of a VDM-SL specification into the PVS specification language using, essentially, the very transparent translation methods described by Agerholm (1996). PVS was used to typecheck the specification and to prove some non-trivial validation conditions. Next, a more abstract specification of the same system was also expressed in PVS, and the original specification was shown to be a refinement of this one. The drawbacks of the translation are that it must be done manually (though automation may be possible), and that the “shallow embedding” technique which is used does not accurately capture the proof rules of VDM-SL. The benefits come from the facts that the portion of VDM-SL which can be represented is substantial and that it is a great advantage to be able to use the powerful PVS proof-checker