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Tracelets and Specifications
(2017)

In the accompanying paper [1] the authors study a model of concurrent programs in terms of events and a dependence relation, i.e., a set of arrows, between them. There also two simplifying interface models are presented; they abstract in different ways from the intricate network of internal points and arrows of program components. This report supplements [1] by presenting full proofs for the properties of the interface models, in particular, that both models exhibit homomorphic behaviour w.r.t. sequential and concurrent composition. [1] B. Möller, C.A.R. Hoare, M.E. Müller, G. Struth: A discrete geometric model of concurrent program execution. In H. Zhu, J. Bowen: Proc. UTP 16. LNCS 10134. Springer 2017, 1-25

A trace of the execution of a concurrent object-oriented program can be displayed in two-dimensions as a diagram of a non-metric finite geometry. The actions of a programs are represented by points, its objects and threads by vertical lines, its transactions by horizontal lines, its communications and resource sharing by sloping arrows, and its partial traces by rectangular figures.