STAIRS towards formal design with sequence diagrams

Abstract

The paper presents STAIRS [1], an approach to the compositional development of UML interactions supporting the specification of mandatory as well as potential behavior. STAIRS has been designed to facilitate the use of interactions for requirement capture as well as test specification. STAIRS assigns a precise interpretation to the various steps in incremental system development based on an approach to refinement known from the field of formal methods and provides thereby a foundation for compositional analysis. An interaction may characterize three main kinds of traces. A trace may be (1) positive in the sense that it is valid, legal or desirable, (2) negative meaning that it is invalid, illegal or undesirable, or (3) inconclusive meaning that it is considered irrelevant for the interaction in question. The basic increments in system development proposed by STAIRS, are structured into three main kinds referred to as supplementing, narrowing and detailing. Supplementing categorizes inconclusive traces as either positive or negative. Narrowing reduces the set of positive traces to capture new design decisions or to match the problem more adequately. Detailing involves introducing a more detailed description without significantly altering the externally observable behavior.

Thread–Based Analysis of Sequence Diagrams

“…Although UML 2.0 tried to provide semantics for every modelling language using a meta-model [Sel04], SDs have only been assigned a behaviour informal semantics according to traditional bMSC semantics. In [Sto03,HHRS05,CK04], formal trace based semantics for SDs were provided and [LS06] solved the semantic problem using an automata-theoretic approach. In [GS05], safety and liveness properties were used for distinguishing valid behaviours from invalid.…”

Underspecification, Inherent Nondeterminism and Probability in Sequence Diagrams

“…However, conceptually there is an important difference between behaviors that are explicitly described and behaviors that are not. Also, positive and inconclusive traces are treated differently by composition operators such as seq (sequential composition) and par (parallel composition), see [HHRS05b].…”

“…As in [HHRS05b], we distinguish between two special cases of refinement, called narrowing and supplementing. Narrowing reduces the set of positive traces to capture new design decisions or to match the problem more accurately.…”

“…STAIRS ([HHRS05b], [RHS05c]) is a method for the compositional development of interactions, such as sequence diagrams and interaction overview diagrams. STAIRS employs two different choice operators to distinguish between underspecification and inherent nondeterminism; alt represents underspecification and xalt represents inherent nondeterminism.…”

“…As these operators are not important for the discussion in this paper, we refer to [HHRS05b] for formal definitions and examples using these operators.…”