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The Object Constraint Language (OCL) 1: IntroductionThe Object Constraint Language [1][2] is a precise textual language to complement graphical languages in modelling object-oriented systems. It allows constraints on the model to be expressed, that can not be expressed using standard diagrammatic notations. Specifically, OCL supports the expression of invariants and pre/post conditions, allowing the modeller to specify precise and detailed constraints on the behaviour of a model, without getting embroiled in implementation detail.OCL is the culmination of recent work in OO modelling [3][4] which has selected ideas from formal methods to combine with diagrammatic, object-oriented modelling resulting in a more precise, robust and expressive notation. Syntropy [3] extended OMT [5] with a Z-like textual language for adding invariants to class diagrams and annotating transitions on state diagrams with pre/post conditions. OCL adopts a simple non-symbolic syntax and restricts itself to a small set of core of concepts.One of the most important aspects of OCL is that it is part of the Unified Modelling Language [6], which has recently become the global standard modelling language, under the auspices of the Object Management Group. As a result it is likely to get much greater exposure and use than previously proposed formal specification languages such as VDM [7] and Z [8], and work invested in ensuring that it is correct and appropriate for its purpose is therefore more likely to reap a dividend than work on the aforementioned languages.The purpose of this paper is to provide a semantics to check that OCL is unambiguous and to improve OCL [9]. As OCL does not exist in a vacuum, but instead depends on some parts of a model to be defined already in diagrams, this necessitates a semantics for a kernel of the UML diagrammatic notation, specifically: class diagrams. Thus OCL provides a focus for integrating the semantics of the diagrammatic notations. We present one such integrated semantics, which we hope lays the foundation for building CASE tools that support integrity checking of whole UML models, not just the component expressed using OCL.Semantics We have chosen to use Larch [20]. This choice is motivated in part by the desire not to be engaged in the design of logics and reasoning systems, but instead to focus on elaborating the meaning of the modelling notations themselves. Larch is a stable language with a well-developed supporting toolset. It uses first-order predicate logic, rather than temporal logic, so is accessible to a wider audience, which includes, hopefully, some commercial tool developers. It is also close to technologies most likely to leverage the sophisticated CASE tools that should result from increasing the precision and expressiveness of model-

Detailed investigations of the transmission performance of adaptively modulated optical orthogonal frequency division multiplexed (AMOOFDM) signals converted using reflective semiconductor optical amplifiers (RSOAs) are undertaken over intensity-modulation and direct-detection (IMDD) single-mode fiber (SMF) transmission systems for WDM-PONs. The theoretical RSOA model adopted for modulating the AMOOFDM signals is experimentally verified rigorously in the aforementioned transmission systems incorporating recently developed real-time end-to-end OOFDM transceivers. Extensive performance comparisons are also made between RSOA and SOA intensity modulators. Optimum RSOA operating conditions are identified, which are independent of RSOA rear-facet reflectivity and very similar to those corresponding to SOAs. Under the identified optimum operating conditions, the RSOA and SOA intensity modulators support the identical AMOOFDM transmission performance of 30Gb/s over 60km SMFs. Under low-cost optical component-enabled practical operating conditions, RSOA intensity modulators with rear-facet reflectivity values of >0.3 outperform considerably SOA intensity modulators in transmission performance, which decreases significantly with reducing RSOA rear-facet reflectivity and optical input power. In addition, results also show that use can be made of the RSOA/SOA intensity modulation-induced negative frequency chirp to improve the AMOOFDM transmission performance in IMDD SMF systems.

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