Invariants, frames and postconditions: a comparison of the VDM and B notations

VDM and B are two “model-oriented” formal methods. Each gives a notation for the specification of systems as state machines in terms of a set of states with operations defined as relations on that set. Each has a notion of refinement of data and operations based on the principles of reduction of nondeterminism and increase in definedness. The paper makes a comparison of the two notations through an example of a communications protocol previously formalized by G. Bruns and S. Anderson (1994). Two abstractions and two reifications of the original specification are given. Particular attention is paid to three areas where the notations differ: the use of postconditions that assume the invariant as opposed to postconditions that enforce it; the explicit “framing” of operations as opposed to the “minimal frame” approach; and the use of relational postconditions as opposed to generalized substitutions