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This section provides fully formal definitions of each of the EDPs in this text, using ?-calculus. Not every aspect of these definitions is explained in full, although you have seen most of the notation used. If you would like a deeper treatment, refer to the base publications for the complete reference, in particular A Theory of Objects [1], which provides the comprehensive foundation you need, as well as SPQR: Formal Foundations and Practical Support for the Automated Detection of Design Patterns from Source Code [35], which provides the original definitions and a much deeper discussion of each. Some minor details have changed since original publication, such as the addition of the explicit naming of the roles in pattern instances. This was found to be of great utility after the original references were published. Each of the following definitions is accompanied by its equivalent PIN diagram so you can immediately see the correlation with the formalism.