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A methodology of program development by transformations is outlined. In particular, ways of representing the transformation rules are discussed, and the relationship between notions of their correctness and the semantic definition of programming languages is studied. How transformation techniques are complemented by the use of abstract data types and assertions is described. In the resulting calculus of transformations, the single rules not only represent design or optimization techniques, but they also incorporate verification principles. To illustrate this approach, the Warshall algorithm is developed by successive applications of transformations.