Offer semantics: Achieving compositionality, flattening and full expressiveness for the glue operators in BIP

Abstract

Based on a concise but comprehensive overview of some fundamental properties required from component-based frameworks, namely compositionality, incrementality, flattening, modularity and expressiveness, we review three modifications of the semantics of glue operators in the Behaviour-Interaction-Priority (BIP) framework. We provide theoretical results and examples illustrating the degree to which the three semantics meet these requirements. In particular, we show that the most recent semantics, based on the offer predicate is the only one that satisfies all of them. The classical and offer semantics are not comparable: there are systems that can be assembled in the classical semantics, but not in the offer one. We present a strict characterisation of the behaviour hierarchy determining the conditions, under which systems in the classical semantics can be transposed into the offer semantics: directly, with minor modifications, by introducing a new type of synchronisation or cannot be transposed at all. The offer semantics allows us to extend the algebras, which are used to model glue operators in BIP, to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T (P ), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T (P ), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.

A Note on the Expressiveness of BIP

“…BIP-like SOS of BIP with the classical semantics defined in [4] and used in the language and code-generation tool-set developed by VERIMAG. 1 In [1], we have provided a counter-example showing that the classical semantics of BIP does not possess flattening, which implies that it does not possess full expressiveness w.r.t. BIP-like SOS either.…”

“…In our previous work [1], we have formalised some of the properties that are desirable for componentbased design frameworks, namely: incrementality, flattening, compositionality and modularity [17,25]. We have also discussed the full expressiveness property, although without providing a formal definition for it.…”

“…In [1], we have studied the satisfaction of the above properties by BIP (Behaviour-Interaction-Priority), which is a component-based framework for the design of correct-by-construction concurrent software and systems based on the separation of concerns between coordination and computation [2,3].…”

“…In [1], we have shown that relaxing the restrictions on priority models to allow arbitrary relations on interactions-rather than strict partial orders on interactions in the interaction model-provides full expressiveness w.r.t. the full class of BIP-like SOS operators.…”

A Theory Agenda for Component-Based Design

“…Besides meeting the universal expressiveness property, BIP meets the incrementality, flattening and compositionality requirements discussed in Section 2.3 (see the detailed discussion in [5]). Glue is a first class entity that can be analysed and composed.…”