A heterogeneous approach to UML semantics

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 so-called 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.