Diagrammatic specification, modelling and programming languages are increasingly prevalent in software engineering and, it is often claimed, provide natural representations which permit of intuitive reasoning. A desirable goal of software engineering is the rigorous justification of such reasoning, yet many formal accounts of diagrammatic languages confuse or destroy any natural reading of the diagrams. Hence they cannot be said to be intuitive. The answer, we feel, is to examine seriously the meaning and accuracy of the terms "natural" and "intuitive" in this context. This paper highlights, and illustrates by means of examples taken from industrial practice, an ongoing research theme of the authors. We take a deeper and more cognitively informed consideration of diagrams which leads us to a more natural formal underpinning that permits (i) the formal justification of informal intuitive arguments, without placing the onus of formality upon the engineer constructing the argument; and (i...

Diagrammatic Modeling Languages (DMLs) are used extensively in software engineering. Well-known examples are DMLs like the Entity-Relationship Diagram (ERD) and its various dialects that are used for datamodeling, the Flowchart, the Statechart and their dialects used for flowbased and state/event-based behavioral-modeling respectively, and the Data-Flow Diagram (DFD) that is used for process-modeling, which incorporates to a degree both data and behavioral perspectives of a system. More recent DMLs include the de-facto industry standard DML suite called the Unified Modeling Language (UML), which contains eight distinct DMLs addressing various views of a system in version 1.5. Another, older and wellestablished standard that may be considered as a three-perspective DML suite is the CCITT/ITU standard Specification and Description Language (SDL). It is worth to mention DMLs that are based upon well-known mathematical formalisms used at system level like the Petri Nets also, as well as diagrammatic formalisms used at an algebraic level (rather than

One emerging approach to reducing the labour and costs of software development favours the specialisation of techniques to particular application domains. The rationale is that programs within a given domain often share enough common features and assumptions to enable the incorporation of substantial support mechanisms into domain-specific programming languages and associated tools. Instead of being machine-oriented, algorithmic implementations, programs in many domain-specific languages (DSLs) are rather user-level, problem-oriented specifications of solutions. Taken further, this view suggests that the most appropriate representation of programs in many domains is diagrammatic, in a way which derives from existing design notations in the domain. This thesis conducts an investigation, using mathematical techniques and supported by case studies, of issues arising from the use of diagrammatic representations in DSLs. Its structure is conceptually divided into two parts: the first is co...