Precise and Formal Metamodeling with the Business Object Notation and PVS

A modeling language consists of both a notation and a metamodel, the latter of which captures the syntactic wellformedness constraints that all valid models must obey. We present two versions of a metamodel for an industrialstrength object-oriented modeling language, BON. The first version of the metamodel, written in BON itself, is intended to give a precise and understandable description of the syntactic well-formedness constraints. The second version, written in the PVS specification language, is intended to give a formal description of the constraints, in a form that is amenable to automated checking and analysis. We demonstrate how the PVS version can be used for conformance checking, i.e., showing that BON models satisfy or fail to satisfy the metamodel. A process is defined for using the metamodel in carrying out conformance testing of models. We also contrast the BON metamodel with the metamodel of the Unified Modelling Language (UML), both in terms of the precise metamodel presented in the UML Semantics Reference, and a formalization of the metamodel presented in the Alloy specification language. We discuss lessons learned in constructing metamodels, particularly in terms of using the PVS specification language for metamodeling. NOTE: the PVS theories discussed in this paper are available from the first author. A web page will be made available at some point that will contain the PVS theories and the most up-to-date version of this document.