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Software architectures and designs "Notations" are typically based on bubble-and-arc diagrams. Embellishing these diagrams may increase their information content but does not make a language. A formal language has syntax, semantics, and inference rules, so that reasoning and automatic manipulation are made possible. The authors describe LePUS, a formal language for describing and reasoning about object oriented software architectures, designs, and patterns. A LePUS formula imposes constraints on the software at an appropriate level of abstraction but does not unnecessarily restrict the implementation. LePUS is not an ad hoc collection of loosely related concepts but instead originates from an insight on a small number of necessary and sufficient basic "Building blocks" that are ubiquitous in object oriented design.
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