UML models consist of several diagrams of different types describing different views of a software system ranging from specifications of the static system structure to descriptions of system snapshots and dynamic behaviour. In this paper a heterogeneous approach to the semantics of UML is proposed where each diagram type can be described in its "natural" semantics, and the relations between diagram types are expressed by appropriate translations. More formally, the UML family of diagram types is represented as a "heterogeneous institution environment": each diagram type is described as an appropriate institution where typically the data structures occurring in a diagram are represented by signature elements whereas the relationships between data and the dynamic behaviour of objects are captured by sentences; in several cases, the diagrams are themselves the sentences. The relationship between two diagram types is described by a socalled institution comorphism, and in case no institution comorphism exists, by a co-span of such comorphisms. Consistency conditions between different diagrams are derived from the comorphism translations. This heterogeneous semantic approach to UML is illustrated by several example diagram types including class diagrams, OCL, and interaction diagrams.

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We present a taxonomy of the variability mechanisms offered by modeling languages. The definition of a formal language encompasses a syntax and a semantic domain as well as the mapping that relates them, thus language variabilities are classified according to which of those three pillars they address. This work furthermore proposes a framework to explicitly document and manage the variation points and their corresponding variants of a variable modeling language. The framework enables the systematic study of various kinds of variabilities and their interdependencies. Moreover, it allows a methodical customization of a language, for example, to a given application domain. The taxonomy of variability is explicitly of interest for the UML to provide a more precise understanding of its variation points.Comment: 15 pages, 14 figures, 1 tabl

An extension of the "Object Constraint Language" (OCL) for modeling real-time and reactive systems in the "Unified Modeling Language" (UML) is proposed, called OCL/RT. A general notion of events that may carry time stamps is introduced providing means to describe the detailed dynamic and timing behaviour of UML software models. OCL is enriched by satisfaction operators @η for referring to the value in the history of an expression at the instant when event η occurred, as well as the modalities always and sometime. The approach is illustrated by several examples. Finally, an operational semantics of OCL/RT is given.

A type inference system and a big-step operational semantics for expressions of the "Object Constraint Language" (OCL), the declarative and navigational constraint language for the "Unified Modeling Language" (UML), are provided; the account is mainly based on OCL 1.4/5, but also includes the main features of OCL 2.0. The formal systems are parameterised in terms of UML static structures and UML object models, which are treated abstractly. It is proved that the operational semantics satisfies a subject reduction property with respect to the type inference system. Proceeding from the operational semantics and providing a denotational semantics, pure OCL 2.0 expressions are shown to exactly represent the primitive recursive functions, whereas pure OCL 1.4/5 expressions are Turing complete.

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Abstract. This paper examines the expressive power of OCL in terms of navigability and computability. First the expressive power of OCL is compared with the relational calculus; it is showed that OCL is not equivalent to the relational calculus. Then an algorithm computing the transitive closure of a binary relation -operation that cannot be encoded in the relational calculus-is expressed in OCL. Finally the equivalence of OCL with a Turing machine is pondered.

The article below presents the insights gained during a number of years of research dedicated to the formalisation of the Unified Modeling Language.