Invariants, frames and postconditions: a comparison of the VDM and B notations
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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 non-determinism and increase in definedness.
This paper makes a comparison of the two notations through an example of a communications protocol previously formalised in [BA91]. 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 generalised substitutions.
KeywordsOperation Definition Generalise Substitution External Behaviour Abstract Specification Coupling Relation
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