Compositional Structuring in the B-Method: A Logical Viewpoint of the Static Context

The B-Method provides a collection of structuring mechanisms which support information hiding, modularisation and compositionality of module operations, although, in order to achieve compositionality and independent (parallel) refinement, sharing is restricted in B. In this paper we elaborate some non-interference and compositionality assumptions that underlie structuring mechanisms such as uses, sees and imports and show how they may be violated by inducing emerging properties which alter the context of the used, seen or imported machine. We discuss how such situations can be avoided by considering necessary and sufficient conditions for logical conservativeness and modularisation. As proof obligations, these conditions ensure that the properties of the context of the seen, used or imported component are conserved, i.e. that they are preserved but not enriched. From a logical viewpoint, these proof obligations require that the uniform interpolant of the contextual extension axioms is implied by the base context.