The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML have a welldefined, fully explored semantics. Such semantics is required in order to ensure that UML concepts are precisely stated and defined. In this paper we describe and motivate an approach to formalizing UML in which formal specification techniques are used to gain insight into the semantics of UML notations and diagrams. We present work carried out by the Precise UML (PUML) group on the development of a precise semantic model for UML class diagrams. The semantic model is used as the basis for a set of diagrammatical transformation rules, which enable formal deductions to be made about UML class diagrams. It is also shown how these rules can be used to verify whether one class diagram is a valid refinement (design) of another. Because these rules are presented at the diagrammatical level, it will be argued that UML can be successfully used as a formal modelling tool without the notational complexities that are commonly found in formal specification techniques.

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Abstract. The current UML semantics documentation has made a signi cant step towards providing a precise description of the UML. However, at present the semantic model it proposes only provides a description of the language's syntax and well-formedness rules. The meaning of the language, which is mainly described in English, is too informal and unstructured to provide a foundation for developing formal analysis and development techniques. Another problem is the scope of the model, which is both complex and large. This paper describes work currently being undertaken by the precise UML group pUML, an international group of researchers and practitioners, to address these problems. A formalisation strategy is presented which concentrates on giving a precise denotational semantics to core elements of UML. This is illustrated through the development of precise de nitions of two important concepts: generalization and packages. Finally, a viewpoint architecture is proposed as a means of providing improved separation of concerns in the semantics de nition.

This paper describes a Meta-Modeling Framework (MMF) that addresses many of the deficiencies in the definition of The unified Modeling Language (UML), and promises to support the OMG's newly announced strategy, Model Driven Architecture (MDA) [OMG01]. The facility comprises a language (MML) for defining modeling notations, a tool (MMT) that checks and executes those definitions, and a method (MMM) consisting of a model based approach to language definition and a set of patterns embodying good practice in language definition.The development of MMF by the pUML group ([pUML]) is ongoing and has been supported by IBM and Rational Inc. The work reported in this paper is a simplified version of the work described in out initial submission to the UML 2.0 revision initiative [Cla01] which is expected to be completed in 2002.The need for the definition of UML are recognized, in part, by the infrastructure RFP for UML 2.0 [OMG00]. In Section 3.0 on page 14 we identify some of the main requirements of the RFP, show how these relate to the needs described above, and outline how MMF addresses them. This paper is structured as follows. The three main components (method, language and tool) to the MMF approach is described. The MMF approach is then applied to a simple description of a modelling language. The language, called SML, is a simplified version of a typical object-oriented static modelling language. MMF allows modelling language properties to be defined as a collection of templates. The templates for SML are defined and then used to construct models of syntax and semantics. Finally we place this work into context and outline future work. A Method for Meta-Modelling (MMM)The UML is a collection of notations, some visual some textual. These notations currently have a loose mapping to an abstract syntax (which is imprecisely defined), which in turn is given an informal semantics written in natural language. The UML needs to become a precisely defined family of modeling languages, where a modeling language comprises a notation (concrete syntax), abstract syntax and semantics.Software Engineers define languages as a collection of models with mappings between them. Typically a language consists of models for concrete syntax, abstract syntax and for the semantic domain. Mappings are defined by associating model elements. A language has mappings between concrete syntax and abstract syntax and between abstract syntax and the semantic domain. For example, a language for class diagrams can be defined in terms of a model for boxes and lines, a model for classes, attributes and associations, and a model for objects and slots. A mapping between abstract and concrete syntax relates classes, attributes and associations to boxes, text and lines. A mapping between abstract syntax and the semantic domain relates classes, attributes and associations to objects and slots.The MMF approach applies OO modelling to the definition of OO modelling languages. Each language component is defined as a package containing a class diagram. Package spec...

The Metamodelling Language (MML) is a subset of the Unified Modeling Language (UML) that is proposed as the core language used to bootstrap the UML 2.0 definition initiative. Since it is metacircular, MML requires an external formal semantics in order to ground it. This paper defines the MML Calculus which is used to formally define MML and therefore provides a semantic basis for UML 2.0.