Concurrency semantics based on metric domain equations

We show how domain equations may be solved in the category of complete metric spaces. For five example languages we demonstrate how to exploit domain equations in the design of their operational and denotational semantics. Two languages are schematic or uni form. Three have interpreted elementary actions involving individual variables and inducing state transformations. For the latter group we discuss three denotational models reflecting a variety of language notions considered. A central theme is the distinction, within the non-uniform setting, of linear time versus branching time models. Throughout, fruitful use is made of the technique of obtaining seman tic mappings, operators, etc. as fixed points of higher-order functions. A brief discussion of the relationship between bisimulation and one of the domains considered concludes the paper.

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